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INDUCTIVE   LOGIC 


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INDUCTIVE    LOGIC 


^^^^;i  Of  ?h, 


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By  JOHN  GEIEE  HIBBEN,  Ph.D. 

ASSISTANT  PROFESSOR  OP  LOGIC   IN   PRINCETON   UNIVERSITY 


NEW  YORK 

CHARLES   SCRIBNER'S  SONS 

1896 


COPYRIGHT,   1896,  BY 
CHARLES  SCRIBNER'S  SONS 


J,  S.  Gushing  &  Co.  —  Berwick  &  Smith. 
Norwood  Mass.  U.S.A. 


CONTENTS 


Chap.  I. — The  Nature  of  Inference      .         .        .         1 

Psychological  and  Logical  Elements  in  Inference,  page  1  ; 
Objective  and  Subjective  Necessity,  4  ;  Data  of  Presen- 
tation, 5 ;  System  as  Ground  of  Inference,  6  ;  The  Im- 
plicit and  Explicit,  11 ;  Inference  mediated  through 
the  Universal,  12  ;  Conceptual  Processes,  13 ;  Explana- 
tion, 14. 

Chap.  II. — Induction  and  Deduction      ...       16 

Various  Opinions  concerning  their  Relative  Importance, 
page  16 ;  Regarded  as  Different  Phases  of  One  and 
the  Same  Process,  17  ;  Their  Relation  to  the  Ground 
of  Inference  regarded  as  a  System,  17  ;  Their  Relation 
to  the  Universal,  18  ;  Difference  between  Truth  and 
Fact,  19 ;  Mutual  Dependence  of  Induction  and  De- 
duction, 20. 

Chap.  III.  —  The  Essentials  of  Induction      .         .       24 

The  Inductive  Hazard,  page  24  ;  Basal  Postulate  of  Induc- 
tion, 25 ;  Its  Epistemelogical  Nature,  26 ;  Induction 
regarded  as  an  Inverse  Process,  27  ;  Law  and  Rule,  30  ; 
Law  in  Terms  of  an  Hypothetical  Universal,  31 ;  Induc- 
tion in  the  Conduct  of  Human  Affairs,  32  ;  The  Scien- 
tific Spirit,  33. 

Chap.  IV.  —  Types  of  Inductive  Inference    .         .       34 

The  Method  of  Enumeration,  page  35 :  a.  Perfect  Induc- 
tion, 36 ;   b.  Incomplete  Enumeration,  37 ;   c.  Proba- 

V 


VI  CONTENTS 

bility,  38 ;  The  Method  of  Analogy,  39 ;  The  Method 
of  Scientific  Analysis,  or  Causal  Determination,  40 ; 
The  Causal  Postulate  underlying  All  the  Methods,  43  ; 
Eelation  of  Mental  Habit  to  Choice  of  Method,  47  ; 
Generalization,  48. 

Chap.  V. — Causation 50 

Logical  Significance  of  the  Causal  Concept,  page  50  ;  Its 
Phenomenal  Significance  —  The  Conservation  of  En- 
ergy, 51 ;  Its  Philosophical  Significance,  53  ;  Its  Logical 
Significance,  54  ;  Its  Epistemelogical  Ground,  58  ;  Pop- 
ular and  Scientific  Idea  of  Cause,  58  ;   Causal  Analysis, 


Chap.  VI. — Causal  Analysis  and  Determination        64 

Sequence,  page  64 ;  Concurrence,  60  ;  Co-existence,  66 ; 
Vital  Growth  and  Development,  68  ;  Collocation,  68 ; 
Different  Modes  of  Transfer  of  Energy,  71 ;  Quantita- 
tive Determination,  72  ;  Observation  and  Experiment, 
73 ;  Negative  Determination,  78 ;  Pseudo-causal  Con- 
nection, 82. 

Chap.  VII. — Mill's  Inductive  Methods  —  The  Method 
or  Agreement 84 

The  Five  Methods,  page  84;  The  Method  of  Agreement, 
86  ;  Symbolic  Kepresentation,  87  ;  Variation  of  In- 
stances, 90  ;  The  Method  of  Agreement  and  Observa- 
tion, 91  ;  Eelation  to  Simple  Enumeration,  91  ;  Se- 
quence and  Co-existence,  92  ;  Defects  of  this  Method, 
93 ;  Its  Chief  Function,  that  of  Suggestion,  96 ;  Illus- 
trations, 97. 

Chap.  VIII.  —  The  Method  of  Difference      .         .     101 

Relation  to  Method  of  Agreement,  page  101  ;  Its  Charac- 
teristics, 101 ;   Symbolic  Representation,  103 ;   Similar 


CONTENTS  vii 

to  Negative  Determination,  104  ;  Relation  to  the  The- 
ory of  Combinations,  105;  Criticisms  of  this  Method, 
106;  Practical  Difficulties,  109;  Illustrations,  113; 
Blind  Experiments,  115. 

Chap.  IX.  —  The  Joint  Method  of  Agreement  and 
Difference 117 

Relation  to  Method  of  Difference,  page  117  ;  Symbolic  Rep- 
resentation, 118;  Difficulty  of  Elimination,  121;  Illus- 
trations, 124  ;  Advantage  of  this  Method  over  the 
Simple  Method  of  Agreement,  128. 

Chap.  X.  — The  Method  of  Concomitant  Variations  130 

Its  Characteristics,  page  130;  Its  Symbolic  Representation, 
131  ;  Quantitative  Determination,  131  ;  Graphic  Repre- 
sentation, 133  ;  Psychological  Impressions,  133  ;  Illus- 
trations, 134;  The  Comprehension  of  the  Intensity  of 
Unknown  Eorces  facilitated  by  this  Method,  141 ;  Lim- 
itations of  this  Method,  142. 

Chap.  XL  —  The  Method  of  Residues     .         .        .     146 

A  Method  of  Elimination,  page  146 ;  Symbolic  Representa- 
tion, 146  ;  A  Deductive  Method,  147  ;  The  Complexity 
of  the  Residual  Element,  148  ;  Illustrations,  149  ;  Re- 
sidual Error  in  Experiments,  153  ;  The  Mental  Habit 
of  inspecting  All  Remainders,  154. 

Chap.  XII. — Verification  and  Prediction     .         .     156 

The  Inducto-deductive  Method,  page  156  ;  Verification,  157  ; 
Prediction,  159  ;  Illustrations,  160  ;  Bacon's  Anticipa- 
tions of  Nature,  163  ;  Scientific  Thought,  164  ;  Indirect 
Method  of  Prediction,  166  ;  Exception  Phenomena,  170; 
Generalization,  171  ;   Mathematical  Method,  172. 


Vlll  CONTENTS 


Chap.  XIII. — Hypothesis 174 

Hypothesis,  as  Preliminary  to  Experiment,  page  174  ;  Hy- 
pothesis, in  place  of  Experiment,  176 ;  Illustrations, 
177  ;  Function  of  the  Imagination  in  Hypothesis,  184  ; 
Analysis  and  Synthesis,  186  ;  Requirements  of  a  Legit- 
imate Hypothesis,  187  ;  Postulate  and  Hypothesis,  189 ; 
Fictions,  106  ;  Suggestions  through  Failure  of  Hypoth- 
eses, 197  ;  Consilience  of  Inductions,  198  ;  Experimen- 
tum  Crucis,  199  ;  AVhewell  and  Mill,  201. 


Chap.  XIY.— Analogy 204 

Analogy  as  Suggestive  of  Inductive  Inquiry,  page  204 ; 
Analogy  in  Generalization,  204  ;  Formation  of  Con- 
cepts and  Analogy,  205 ;  Natural  Kinds,  205  ;  Classifi- 
cation, 207  ;  Teleology,  208  ;  False  Analogies,  220. 

Chap.  XV. —Probability 226 

Complexity  of  the  Causal-nexus,  page  226  ;  Relation  to 
Enumerative  Induction,  228  ;  Calculation  of  the  Proba- 
bility of  a  Particular  Event,  230  ;  Adverbial  Probabil- 
ity, 232 ;  Estimate  of  Aggregates,  234  ;  Chance  and 
Coincidence,  243  ;  Circumstantial  Evidence,  247  ;  Rela- 
tion to  the  Method  of  Residues,  251. 


Chap.  XVI.  —  Empirical  Laws  ....     252 

Three  Classes  of  Laws  of  Varying  Degree  of  Probability, 
page  252 ;  Empirical  Law  as  Expression  of  Causal 
Relation  in  Process  of  Determination,  253 ;  Colloca- 
tions giving  Rise  to  Empirical  Laws,  254  ;  Generaliza- 
tions expressing  an  Aggregate  of  Qualities  in  the  Same 
Individual,  256  ;  Probability  and  Empirical  Laws,  258 ; 
The  Method  of  Agreement,  259  ;  The  Empirical  Nature 
of  the  Causal  Relation,  260. 


CONTENTS 


Chap.  XVIL— Fallacies 262 

Of  Perception,  page  263  :  a.  Failure  to  comprehend  the 
Entire  Field  of  Vision,  263  ;  h.  Failure  to  concentrate 
Attention,  265 ;  c.  Errors  due  to  Apperceptive  Projec- 
tion, 266  ;  Of  Judgment,  266 :  a.  False  Associations, 
267  ;  h.  Emotional  Perturbation,  267  ;  c.  General  Frail- 
ties of  Human  Nature,  Bacon's  Idols,  269;  Of  Imagi- 
nation, 271 ;  Of  the  Conceptual  Processes,  275  :  a.  Hasty 
Generalization,  276  ;  6.  Interpolation  in  a  Series,  277 ; 
c.  Provincialisms,  278  ;  d.  False  Analogies,  278  ;  e.  In- 
correct Classification,  279 ;  Psychological  Character  of 
these  Fallacies,  279. 

Chap.  XVIII.  —  The  Inductive  Methods  as  applied  to 
THE  Various  Sciences 281 

Nature  of  Method  v?ill  vary  with  Nature  of  the  Phenomena, 
page  281  ;  Complication  of  the  Doctrine  of  the  Conser- 
vation of  Energy,  287  ;  The  Phenomena  of  One  Science 
to  be  interpreted  in  the  Light  of  the  Results  of  Another 
Science,  290  ;  Growing  Tendency  to  supplement  Deduc- 
tive Method  by  Inductive,  292. 

Chap.  XIX. — Historical  Sketch  of  Induction      .     297 

Socrates,  297  ;  Plato,  297  ;  Aristotle,  298  ;  Roger  Bacon, 
300 ;  Leonardo  da  Vinci,  301 ;  Telesius,  302  ;  Campa- 
nella,  303 ;  Csesalpinus,  Copernicus,  Gilbert,  Kepler, 
Brah6,  Galileo,  304  ;  Francis  Bacon,  304  ;  Locke,  307  ; 
Newton,  307;  Herschel,  308;  Whewell,  310;  Mill,  311. 

Chap.  XX.  —  Logical  Exercises       ....     313 


PREFACE 

It  has  been  my  aim,  in  the  following  pages,  to 
present  the  essential  features   of   inductive  logic, 
in  the  hope  that  this  work  may  prove  a  fitting 
supplement  to  the  elementary  courses  in  formal  or 
deductive  logic.     The  impression  is  too  often  left 
in  the   minds    of    those   who   have    pursued    the 
study  of  deductive  logic  exclusively  that  the  for- 
mal  laws   of  the   syllogism   constitute  the  entire 
body  of  logical  doctrine,  and  that  reasoning  con- 
sists   solely   in    drawing   conclusions   from   given 
premises.      There   is   danger   here    lest    reasoning 
become    associated    with    an    artificial    procedure 
that  seems  to  find  its  proper  sphere  in  the  solu- 
tion of   verbal   quibbles    and   logical  puzzles.     In 
the    actual   experiences    of    life,   Ave   do   not  find 
our   premises   ready   made.     They   are   the   result 
of  wide  observation  and  patient  investigation  and 
experiment.       We    challenge    premises    that    are 
given,   and  weigh  their    significance.      We    meet 
particular   facts   before   we   do   the   general    laws. 


Xll  PREFACE 

The  former  must  be  tested  and  interpreted,  before 
we  can  rise  to  the  general  laws  which  underlie 
them,  and  Avhich  may  stand  as  the  major  prem- 
ises of  our  syllogisms.  Thus  within  the  very 
sphere  of  deduction  itself  there  naturally  opens 
a  wide  field  for  inductive  inquiry.  Therefore  I 
have  emphasized  the  necessity  of  a  thorough 
knowledge  of  the  principles  of  inductive  logic 
in  order  to  comprehend  the  material  as  well  as 
the  formal  elements  in  inference,  and  without 
which  no  firm  grasp  of  the  general  process  of 
reasoning  is  possible.  I  have  also  insisted  upon 
regarding  induction  and  deduction  as  mutually 
dependent ;  not  as  separate  modes  of  inference, 
but  rather  as  different  phases  of  one  and  the 
same  logical  procedure. 

I  have  endeavored,  also,  to  indicate  in  some 
measure  at  least,  the  salient  characteristics  of 
the  modern  logic,  especially  as  presented  in  the 
works  of  Lotze,  Sigwart,  Jevons,  Green,  Bosan- 
quet,  and  Venn.  In  the  illustrations  of  the 
various  inductive  methods  I  have  sought  fresh 
material  as  far  as  possible,  with  the  view  of 
representing  the  actual  modes  of  reasoning  and 
methods  of  investigation  employed  by  those  who 
have  become  eminent  in  their  several  spheres  of 
research,  such  as  Faraday,  Tyndall,  Darwin,  and 


PREFACE  xiii 

Lubbock;  and  especially  the  different  methods 
which  have  led  to  important  discoveries  in  the 
various  sciences.  This  applies  not  only  to  the 
illustrations  in  the  text  proper,  but  also  to  those 
which  I  have  collected  in  Chapter  XX.  under  the 
head  of  Logical  Exercises.  It  seems  to  me, 
moreover,  that  inasmuch  as  the  principles  of 
inductive  investigation  are  in  such  accord  with 
the  scientific  spirit  of  our  age,  their  importance 
as  a  logical  discipline  cannot  be  too  highly  valued. 

J.  G.  H. 
Princeton,  N.J.,  March  2,  1896. 


INDUCTIVE   LOGIC 

CHAPTEK  I 

The  Nature  of  Inference 

Induction  is  a  particular  mode  of  inference  in 
general ;  and  therefore  before  its  nature  and  scope 
can  be  adequately  defined,  it  will  be  necessary  to 
give  some  account  of  the  theory  of  inference,  and 
its  X3recise  logical  signification.  Moreover,  it  is  not 
possible  to  appreciate  the  distinction  between  the 
processes  of  induction  and  deduction,  until  we  have 
first  examined  the  characteristic  features  which 
are  common  to  the  two,  and  which  constitute  the 
essential  elements  of  inference  itself.  The  nature 
of  inference  may  be  unfolded  in  two  ways.  We 
may  consider  what  it  is  in  its  outward  aspect  — 
that  is,  through  its  phenomenal  manifestation  in 
what  it  effects ;  or  it  may  be  more  strictly  defined 
in  terms  of  its  warrant,  or  ground.  From  the  first 
point  of  view  we  examine  inference  as  regards  its 
psychological  significance;  that  is,  what  is  infer- 
ence considered  as  a  psychical  experience,  its  na- 
ture and  characteristics?  But  we  must  consider 
also   the   second   question,  whether   there   is    any 

B  1 


2  INDUCTIVE  LOGIC 

necessity  limiting  and  determining  the  subjective 
experience,  which  presents  the  character  of  a  law 
having  universal  validity.  AVhat  goes  on  in  the 
mind  during  the  process  of  inference  ?  Also,  what 
is  the  rationale  of  such  a  process?  These  ques- 
tions we  will  examine  more  closely,  in  order  to 
show  the  nature  of  inference  under  the  two  aspects, 
the  one  psychological,  and  the  other  logical. 

It  is  a  well-recognized  fact  in  psychology,  that 
in  our  simplest  as  well  as  the  more  complex  per- 
ceptions, the  interpretation  of  the  data  of  presenta- 
tion always  goes  beyond  the  strict  content  of  the 
data  themselves.  We  see  more  than  is  given  in 
the  field  of  vision  immediately  before  us.  The 
mind  supplies  here  and  there  the  necessary  parts 
that  are  lacking  in  the  actual  elements  of  presenta- 
tion, and  yet  which  are  necessitated  by  the  known 
nature  of  that  which  is  actually  given.  We  form 
our  judgment  of  distance  indirectly,  and  not  through 
direct  presentation.  So,  also,  our  idea  of  a  third 
dimension  is  acquired  by  a  process,  marvellously 
complex,  in  which  the  data  both  indicate  and  yet 
are  transcended  by  the  results.  Whether  the  nativ- 
ist  or  empiricist  holds  the  true  position  concern- 
ing original  psychical  experience,  it  still  must  be 
conceded  according  to  either  theory  that  the  devel- 
opment of  our  perceptions  corresponds  to  a  law  of 
growth  based  upon  accumulated  inferences.  Infer- 
ence has  been  defined  as  the  indirect  reference  of 
a  content  to  reality,  and  as  such,  we  see  the  be- 
ginnings of  inference  in  the  most  simple  of  our 
perceptions.      Every  perception  contains  a  direct 


THE  NATURE  OF   INFERENCE  3 

reference  to  reality,  but  also  something  wliicli  in 
a  greater  or  less  degree  is  referred  indirectly  to 
reality.  The  fact  that  our  knowledge  as  given  in 
the  complete  percej^tion  contains  more  than  is  actu- 
ally mediated  through  the  avenues  of  the  senses, 
is  due  to  the  apperceptive  processes  of  conscious- 
ness. Mind  is  active  in  perception,  and  not  a  mere 
passive  receptacle.  That  which  is  given,  the  raw 
material  of  the  senses,  is  elaborated  and  extended, 
as  it  is  combined  with  the  wealth  of  representative 
and  conceptual  material  which  the  mind  brings  to 
every  new  perception.  To  this  extent,  at  least,  the 
mind  possesses  a  creative  function.  A  certain 
appearance  of  sky,  combined  with  peculiar  condi- 
tions of  mind  and  temperature,  leads  one  to  assert, 
with  some  degree  of  certitude,  that  it  will  rain 
before  morning.  The  prediction  is  an  inference 
based  upon,  and  growing  out  of,  the  actual  data 
of  perception,  and  yet  far  outrunning  them.  We 
recognize  a  friend  from  his  step  or  voice.  The 
mere  presentation  is  only  a  sound.  That  it  is 
associated  with  a  person,  and  not  an  animal,  or  a 
thing,  is  an  inference;  that  this  is  the  particular 
person  whom  we  recognize  as  a  friend  and  can  call 
by  name,  even  before  we  turn  around  to  confirm 
the  opinion  by  direct  testimony  of  vision,  this  is 
a  still  further  inference.  And  even  when  we  open 
our  eyes  in  simple  vision  itself,  we  fill  up  many 
a  gap  in  our  minds,  and  give  depth  and  distance, 
and  interpret  the  contrasts  of  light  and  shade,  and 
the  play  of  colors,  through  the  process  of  inference, 
although  we  may  not  be  aware  of  the  process  itself, 


4  INDUCTIVE  LOGIC 

which  is  automatically  operative  through  long-con- 
tinued habit.  When  we  thus  regard  inference  as 
a  psychological  phenomenon,  it  may  be  readily  ex- 
plained by  the  laws  of  comparison,  association, 
recognition,  generalization,  etc.  And,  as  such,  in- 
ference has  a  subjective  force  at  least,  and  leads  to 
the  habit  of  prediction  and  expectation.  The  will, 
influenced  by  the  resulting  belief,  leads  to  activi- 
ties consistent  with  such  expectation. 

Here,  however,  the  question  arises,  which  is 
urged  with  such  force  by  Hume,  Is  there  objective 
validity  as  well  as  subjective  necessity  ?  This 
leads  to  a  consideration  of  inference,  from  the  sec- 
ond point  of  view,  above  mentioned.  We  may  be 
constrained  to  believe  certain  things  concerning  the 
great  world  lying  beyond  the  sphere  of  immediate 
consciousness;  but  what  warrant  have  we  in  so 
doing,  or  what  assurance  that  our  conclusions  are 
correct  ?  May  we  not  be  deceived,  after  all,  and  by 
some  psychological  trick  be  led  to  regard  the  phe- 
nomena of  consciousness  as  quite  otherwise  than 
that  which  obtains  in  reality?  We  may  have  a 
strong  aversion  to  sitting  down  at  a  table  where 
the  number  of  persons  will  be  thirteen.  But  has 
the  subjective  conviction,  that  one  of  the  thirteen 
will  die  in  the  course  of  the  year,  any  value  when 
we  come  to  refer  it  to  reality,  and  ask  ourselves  the 
nature  of  the  ground  upon  Avhich  the  conviction  is 
based  ? 

On  the  other  hand,  however,  it  is  quite  a  differ- 
ent kind  of  necessity  which  constrains  us  to  judge 
that  if  a  person  jumps  off  of  the  roof  of  a  house, 


THE  NATURE  OF  INFERENCE  5 

he  must  surely  fall  to  the  ground  below.  Some 
grossly  superstitious  and  ignorant  people  may  be- 
lieve the  former  with  as  obstinate  a  conviction  as 
the  latter,  so  that  a  purely  psychological  criterion 
of  the  strength  of  conviction  is  not  at  all  adequate 
or  satisfactory.  Is  there  any  other  criterion  ?  In 
what  instances  does  this  subjective  constraint  pro- 
ceed from  the  necessities  of  reality  ?  or,  in  other 
words,  in  what  cases  are  we  able  to  discover  a  logi- 
cally grounded  warrant  which  compels  the  infer- 
ence, in  distinction  from  the  mere  psychological 
compulsion  which  is  occasioned  by  the  psychical 
tendencies  of  association  and  generalization  ? 

This  leads  us  to  consider  the  logical,  in  distinction 
from  the  psychological,  nature  of  inference.  Inas- 
much as  the  characteristic  feature  of  inference  con- 
sists in  this,  that  while  depending  upon  certain  data 
of  presentation,  it  nevertheless  wholly  transcends 
them,  the  question  naturally  suggests  itself,  whether 
it  is  something  within  the  data  themselves,  or  with- 
out, by  virtue  of  which  the  mind  thus  goes  beyond 
them  in  the  process  of  inference.  If  it  lies  wholly 
without  the  data,  it  must  be  something  imposed 
upon  them  by  the  mind,  and  as  such  can  have  only 
a  psychological  force  and  value.  For  instance,  the 
belief  that  if  thirteen  sit  down  together  at  a  table, 
one  will  die  in  the  course  of  the  year,  can  have  only 
a  subjective  value  and  significance.  This  is  true  in 
all  cases  where  the  necessity  of  conviction  finds  its 
origin  in  prejudice  or  in  superstition,  or  it  may  be 
in  the  force  of  authority.  In  all  such  instances  we 
feel  the  lack  of  a  satisfactory  logical  ground.    How- 


6  INDUCTIVE  LOGIC 

ever,  on  the  other  hand,  if  the  data  of  consciousness 
contain  within  themselves  that  which  enables  us  to 
transcend  them  at  the  same  time  that  we  interpret 
them,  there  is  external  validity  for  our  inference 
that  has  a  logical  worth.  This  seems  at  the  first 
glance  to  be  a  paradox.  How  can  any  content 
enable  us  to  state  concerning  it  more  than  is  con- 
tained within  it  ?  The  answer  to  the  seeming  para- 
dox is  that  every  concept,  and  every  perception  as 
well,  have  both  an  explicit  and  implicit  content.  We 
never  attain  complete  vision  or  perfect  apprehension. 
There  are,  moreover,  many  points  of  view,  each 
giving  additional  knowledge  concerning  any  phe- 
nomenon present  in  consciousness.  We  see,  there- 
fore, only  in  part,  and  yet  that  which  is  seen  contains 
certain  necessary  implications  concerning  that  which 
is  not  seen.  In  the  progress  of  knowledge,  subse- 
quent observations,  different  points  of  view,  are  ever 
confirming  and  amplifying  our  inferences,  enabling 
us  to  perceive  immediately  what  formerly  was  only 
inferred.  The  process  by  which  the  implicit  is 
becoming  explicit  indicates  a  necessary  relation 
existing  between  that  which  is  known  mediately 
and  that  which  is  known  immediately.  Moreover, 
consciousness  has  been  represented  as  a  stream,  or  an 
intricately  interwoven  web,  —  something  extremely 
complex.  Every  part  is  related  both  proximately 
and  remotely.  There  is  no  such  thing  as  an  isolated 
perception ;  every  perception  has  its  complex  rela- 
tions and  connections.  So  also  every  concept  which 
is  f  oruied  by  generalization  through  comparison  and 
abstraction,  of  our  presentations  as  interpreted  by 


THE  NATURE   OF  INFERENCE  7 

US,  possesses  this  characteristic  of  greater  or  less 
complexity.  In  this  manner  the  world  of  conscious- 
ness is  constructed ;  that  is,  the  world  as  it  is  for  us. 
This  forms  a  complex  whole  made  up  of  parts,  which 
in  themselves  may  be  regarded  as  Avholes,  and  yet 
which  may  be  still  further  divided  and  subdivided. 
Such  an  interrelated  whole  we  may  style  a  sys- 
tem, or,  in  other  words,  a  complex  whole  whose  parts 
are  congruently  arranged.  The  idea  of  system  finds 
expression  in  the  "Law  of  Totality,"  —  that  our 
knowledge  is  capable  of  arrangement  in  a  self-con- 
sistent and  harmonious  system,  and  which  moreover 
in  its  content  and  form  faithfully  represents  objec- 
tive reality.^  We  find,  therefore,  that  in  the  focus 
of  consciousness  at  any  one  time,  whether  in  the 
sphere  of  presentation  or  in  the  region  of  representa- 
tive or  the  conceptual  processes,  whatever  is  given 
carries  with  it  always  certain  implications,  and  there- 
fore certain  necessary  relations.  This  is  specially 
emphasized  in  Bosanquet's  definition  of  system: 
"System  is  a  group  of  relations,  or  properties,  or 
things,  so  held  together  by  a  common  nature  that 
you  can  judge  from  some  of  them  what  the  others 
must  be."  ^  Two  facts  regarded  as  independent  and 
considered  separately  may  give  no  information  be- 
yond their  explicit  contents ;  but  when  conjoined, 
they  imply  more  than  the  sum  of  their  parts.  How 
often  two  ideas  in  separate  minds  yield  no  result ; 
but   brought   together,  they  give   light.     Isolation 

1  Ueberweg,  A  System  of  Logic  and  History  of  Logical  Doc- 
trine, pp.  540  f . 

2  Bosanquet,  The  Essentials  of  Logic,  p.  140. 


S  INDUCTIVE  LOGIC 

negatives  inference.  To  unfold  any  data  in  all 
their  manifold  implications  is  the  process  of  infer- 
ence. Its  warrant  lies  in  the  fundamental  postulate 
of  knowledge  which  we  are  constrained  to  assume; 
namely,  that  our  consciousness  must  be  self-con- 
sistent throughout.  Whatever  is  admitted  as  true 
must  find  a  congruent  place  in  the  system  to  which 
it  is  possible  to  refer  it.  The  necessity  of  fitting  it 
in  its  proper  place  gives  rise  to  certain  implications 
which  necessitate  corresponding  relations  and  attri- 
butes. And  if  it  could  not  be  put  into  such  a  place, 
we  would  feel  that  we  should  have  to  surrender  the 
idea  of  self-consistency  in  the  variously  related  ele- 
ments of  our  consciousness.  The  very  integrity  of 
our  mental  life  necessitates  this  conviction. 

Therefore  a  part  being  given,  we  supply  in  our 
minds  other  parts,  or  the  whole  to  which  the  given 
part  must  necessarily  belong.  To  achieve  this,  with 
logical  warrant,  our  knowledge  of  the  part  must  be 
adequate  to  the  extent  that  we  know  that  the  ele- 
ment under  consideration  cannot  be  complete  in 
itself,  but  must  be  supplemented  by  its  appropri- 
ately related  elements  which  with  it  go  to  make  up 
the  complete  system.  We  infer  the  nature  of  the 
flower  not  yet  in  bud,  by  the  sprouting  leaf.  The 
one  necessitates  the  other  by  virtue  of  their  com- 
mon inherence  in  the  same  plant  system.  We 
know  that  figs  do  not  come  from  thorns,  nor  grapes 
from  thistles.  Columbus,  noting  the  seaweed,  and 
birds,  and  the  drift  of  the  sea,  inferred  a  shore 
beyond,  to  which  he  was  constrained  by  the  neces- 
sities of  thought  to  refer  them.     It  is  said  of  Cuvier 


THE  NA.TURE  OF  INFERENCE  9 

that  lie  was  able  to  reconstruct  part  for  part  the 
entire  frame  and  organism  of  an  animal  whose 
fossil  tooth  alone  formed  the  original  datum.  He 
knew  the  system  to  which  it  must  have  belonged 
and  to  which  it  alone  could  possibly  be  referred. 
An  interesting  quotation  from  Cuvier  himself  illus- 
trates most  appropriately  this  function  of  inference. 
He  says  in  his  Ossemens  Fossiles,  "I  doubt  if  any 
one  would  have  divined,  if  untaught  by  observation, 
that  all  ruminants  have  the  foot  cleft,  and  that  they 
alone  have  it.  I  doubt  if  any  one  would  have 
divined  that  there  are  frontal  horns  only  in  this 
class ;  that  those  among  them  which  have  sharp 
canines  for  the  most  part  lack  horns.  However, 
since  these  relations  are  constant,  they  must  have 
some  sufficient  cause  ;  but  since  we  are  ignorant  of 
it  we  must  make  good  the  defect  of  the  theory  by 
means  of  observation:  it  enables  us  to  establish 
empirical  laws  which  become  almost  as  certain 
as  rational  laws  when  they  rest  on  sufficiently 
repeated  observations ;  so  that  now  whoso  sees 
merely  the  print  of  a  cleft  foot  may  conclude  that 
the  animal  which  left  this  impression  ruminated, 
and  this  conclusion  is  as  certain  as  any  other  in 
physics  or  morals.  This  footprint  alone,  then, 
yields  to  him  who  observes  it  the  form  of  the 
teeth,  the  form  of  the  jaws,  the  form  of  the  verte- 
brae, the  form  of  all  the  bones  of  the  legs,  of  the 
thighs,  of  the  shoulders,  and  of  the  pelvis  of  the 
animal  which  has  passed  by."^ 

In  the  common  conduct  of  every-day  life  we  infer 
1  Quoted  by  Jevons,  Principles  of  Science,  2d  ed.  p.  G83. 


10  INDUCTIVE  LOGIC 

beyond  the  immediate  present  experience  to  future 
happenings  and  in  a  simihir  manner.  My  train  is 
half  an  hour  late.  I  know  I  must  miss  my  connec- 
tions at  the  station  ahead ;  for  the  train  I  am  hop- 
ing to  catch  at  that  place  is  scheduled  to  leave  live 
minutes  after  the  time  of  arrival  of  the  train  I  am 
now  on.  The  time  relations  here  necessitate  my 
missing  my  connections.  This  is  rendered  still 
more  certain  if  they  are  rival  roads ;  on  no  account 
will  one  wait  for  the  other.  Moreover,  the  train  I 
hope  to  make  is  made  up  and  leaves  the  station  in 
question,  and  so  I  cannot  fall  back  upon  the  favoring 
chance  that  it  also  may  be  detained  en  route,  and 
so  enable  me,  after  all,  to  reach  it  in  time.  Thus, 
with  every  additional  knowledge  of  the  system  which 
forms  the  ground  of  my  inference,  and  the  various 
conditions  which  affect  it,  the  validity  of  my  infer- 
ence is  thereby  increased.  Inference  regarded  as 
the  analysis  of  a  system  of  interrelated  parts  is 
illustrated  in  the  following  paragraph  of  Professor 
James  :  "  The  results  of  reasoning  may  be  hit  upon 
by  accident.  Cats  have  been  known  to  open  doors 
by  pulling  latches,  etc.  But  no  cat,  if  the  latch  got 
out  of  order,  could  open  the  door  again,  unless  some 
new  accident  at  random  fumbling  taught  her  to  asso- 
ciate some  new  total  movement  with  the  total  phe- 
nomenon of  the  closed  door.  A  reasoning  man, 
however,  would  open  the  door  by  first  analyzing  the 
hindrance.  He  would  ascertain  what  particular 
feature  of  the  door  was  wrong.  The  lever,  e.g., 
does  not  raise  the  latch  sufficiently  from  its  slot  — 
case  of  insufficient  elevation  —  raise  door  bodily  on 


THE  NATURE   OF   INFERENCE  11 

hinges !  Or  door  sticks  at  top  by  friction  against 
lintel — press  it  bodily  down!  I  have  a  student's 
lamp  of  which  the  flame  vibrates  most  unpleasantly 
unless  the  collar  which  bears  the  chimney  be  raised 
about  a  sixteenth  of  an  inch.  I  learned  the  remedy 
after  much  torment,  by  accident,  and  now  always 
keep  the  collar  up  with  a  small  wedge.  But  my 
procedure  is  a  mere  association  of  two  totals,  dis- 
eased object  and  remedy.  One  learned  in  pneumat- 
ics could  have  named  the  cause  of  the  disease  and 
thence  inferred  the  remedy  immediately."  ^ 

Inference,  therefore,  may  be  regarded  as  a  deep 
penetrating  insight.  The  explicit  is  that  wdiich 
lies  upon  the  surface,  which  the  mind  immediately 
grasps,  for  it  lies  directly  in  the  focus  of  conscious- 
ness. Whereas  the  implicit  is  beneath  the  surface, 
and  is  revealed  only  through  a  searching  analysis. 
This  difference  may  be  exhibited  through  the  dis- 
tinction between  the  actual  and  the  potential.  A 
child  regards  gunpowder  merely  as  a  pile  of  coarse- 
grained sand.  The  man  sees  what  the  child  sees, 
but  also  the  existing  possibilities  under  certain  con- 
ditions of  explosive  force.  He  apprehends  the 
potential  as  well  as  the  actual ;  and  his  inference 
as  to  the  possible  results  is  based  upon  his  superior 
insight.  It  is  therefore  the  well-furnished  mind 
which  sees  things  as  most  widely  related,  and  dis- 
cerns the  potential  as  well  as  the  actual  manifesta- 
tion, which  will  prove  the  most  fertile  in  accurate 
inference,  in  prophetic  suggestion,  and  in  inventive 
resource. 

1  James,  Psychology,  Vol.  II.  pp.  339,  340. 


12  INDUCTIVE  LOGIC 

The  whole  world  of  reality,  as  well  as  that  of 
knowledge,  may  be  considered  as  one  system,  em- 
bracing within  the  unity  of  its  totality  all  the  vari- 
ous systems  with  their  complicated  parts.  From 
this  point  of  view  everything  bears  relations  to 
everything  else  in  the  universe.  The  original  sig- 
nification of  the  term  universe  is  thus  emphasized. 
This  thought,  no  doubt,  Tennyson  had  in  mind  in 
the  following  verse :  — 

Flower  in  the  crannied  wall, 

I  pluck  you  out  of  the  crannies, 

I  hold  you  here,  root  and  all,  in  my  hand. 

Little  flower  —  but  ifl  could  understand 

What  you  are,  root  and  all,  and  all  in  all, 

I  should  know  what  God  and  man  is. 

We  can,  in  this  connection,  best  exhibit  the  pre- 
cise nature  and  function  of  the  universal  in  infer- 
ence. The  possibility  of  unfolding  the  properties 
or  relations  of  anything  in  all  its  implications 
depends  upon  our  knowledge  of  the  universal  con- 
cept to  which  the  properties  or  relations  in  ques- 
tion are  naturally  referred.  AVhile  a  singular 
proposition  is  the  statement  of  the  mere  occur- 
rence of  a  phenomenon,  the  universal  always 
implies  a  knowledge  of  the  conditions  and  rela- 
tions of  the  phenomenon.^  Insight  is  only  pos- 
sible where  there  is  a  wealth  of  universal  concepts. 
We  see  an  animal  which  we  observe  to  be  cloven- 
footed.  We  infer  that  it  also  chews  its  cud.  We 
do  not  observe  this.     The  assertion  does  not  arise 

1  See  Green,  Philosophical  Works,  Vol.  II.  pp.  284,  285. 


THE  NATURE  OF  INFERENCE  13 

directly  from  observed  reality,  but  indirectly 
through  the  generic  concept  that  has  grasped  to- 
gether the  two  attributes  of  chewing  the  cud  and 
cloven  feet  as  always  and  necessarily  coexisting 
in  one  and  the  same  animal  Inference,  in  this 
sense,  may  be  regarded  as  the  indirect  reference 
of  knowledge  to  reality,  and  this  is  always  medi- 
ated through  the  universal.  The  universal  has 
this  characteristic  feature,  that  it  preserves  an 
identity  in  the  midst  of  manifold  differences.  The 
same  thought  may  be  expressed  by  saying  that  the 
universal  manifests  a  unity  in  the  midst  of  diver- 
sity. However  widely  different,  in  many  respects, 
the  animals  may  appear  that  chew  the  cud,  —  as 
the  cow,  deer,  sheep,  etc.,  —  there  is  always  the 
constant  characteristic  that  they  are  cloven-footed. 
Such  a  point  of  identity  furnishes  the  constant 
factor  which  determines  the  nature  and  the  validity 
of  the  inference.  Were  it  not  for  this  conceptual 
power  of  the  mind,  this  ability  to  grasp  phenom- 
ena in  their  universal  essence,  and  consider  them 
as  interrelated  and  connected,  we  could  never  pass 
beyond  individual  and  particular  experiences  which 
would  form  a  series  of  wholly  disconnected  events. 
Knowledge  could  not  then  form  a  self-consistent 
system,  or  inference  possess  any  higher  worth  than 
a  haphazard  guess.  As  Green  says,  "A  'mere 
fact,'  a  fact  apart  from  relations  which  are  not  sen- 
sible, would  be  no  fact,  would  have  no  nature,  would 
not  admit  of  anything  being  known  or  said  about 
it."i 

1  Green,  Philosophical  Works,  Vol.  IL  p.  301. 


14  IXDUCXn^  LOGIC 

Moreover,  iufereuce  is  not  merely  employed  to 
extend  tlie  field  of  consciousness  in  unfolding  sup- 
plementary elements  lying  beyond  the  sphere  of 
direct  cognition;  the  elements  may  all  be  given 
immediately,  and  inference  employed  to  discover 
their  connection  and  interrelations,  by  virtue  of 
what  bond  they  belong  in  one  or  the  same  sys- 
tem. Inference  here  functions  as  explanation.  A 
man  is  found  dead;  there  are  mauy  wounds  upon 
his  person,  evidences  of  a  struggle  in  an  out-of-the- 
way  place  upon  a  lonely  road.  Such  a  combina- 
tion of  facts  calls  for  an  explanation  which  shall  be 
consistent  with  them.  The  facts  must  all  be  cor- 
related in  a  system  whose  related  facts  and  the 
unity  of  the  whole  will  completely  satisfy  the 
mind.  The  mind  is  satisfied  only  Avhen  all  hang 
together  in  what  seems  the  only  possible  self- 
consistent  co-ordinated  system.  The  facts  being 
given,  they  must  be  read  backward  to  their  origin. 
The  other  aspect  of  inference  is  the  reading  of 
facts  forwards,  or  unfolding  them  in  their  neces- 
sary consequences.  Inference  is  the  reply  to  the 
natural  questions  of  the  mind,  —  whence  and 
whither  ?  And  the  process  is  essentially  the  same, 
whether  its  peculiar  mode  consists  in  the  evolu- 
tion or  the  involution  of  that  which  is  given  in 
consciousness. 

^loreover,  the  mere  psychological  inference,  the 
subjective  extension  of  the  data  of  consciousness 
without  any  objective  ground  or  warrant,  should 
ever  be  corrected,  or  even  at  times  wholly  set  aside 
by  means  of  the  truly  logical  inference.     Where 


THE  NATURE  OF  INFERENCE  15 

the  psychological  experience,  in  transcending  simple 
presentation,  proceeds  npon  strictly  logical  gronnds, 
and  has  objective  validity  as  well  as  subjective 
necessity,  we  possess  a  warrant  of  the  highest  pos- 
sible worth. 


CHAPTER  II 
Induction  and  Deduction 

There  have  been  divergent  tendencies  in  the 
history  of  logic,  to  make  either  deduction  or  in- 
duction alone  the  whole  of  logical  procedure  in  the 
process  of  inference.  The  fact  that  the  Aristotelian 
logic,  which  is  essentially  deductive,  has  been  for 
centuries  exclusively  associated  with  logic  as  a 
whole,  has  left  the  impression  upon  many  minds 
that  it  is  the  beginning  and  end  of  the  logical  en- 
cyclopaedia. On  the  other  hand,  J.  S.  Mill  and  his 
followers  have  attempted  to  analyze  the  syllogism 
to  prove  its  essentially  inductive  character;  and 
they  have  maintained  that  all  reasoning  is  induc- 
tive. This  is  the  position  in  the  main  of  Bacon, 
Locke,  and  Bain.  Locke,  for  instance,  insists  that 
the  syllogism  is  of  less  value  than  external  and 
internal  experience,  induction,  and  common  sense. ^ 

So  also,  in  a  similar  vein,  Schleiermacher  says: 
"The  syllogistic  procedure  is  of  no  vakie  for  the 
real  construction  of  judgments,  for  the  substituted 
judgments  can  only  be  higher  and  lower;  nothing 
is  expressed  in  the  conclusion  but  the  relation  of 
two  terms  to  each  other,  which  have  a  common 

1  Essay  on  Human  Understanding,  Book  IV.  p.  7. 
16 


INDUCTION  AND  DEDUCTION  17 

member,  and  are  not  without,  but  within,  each 
other.  Advance  in  thinking,  a  new  cognition,  can- 
not originate  by  the  syllogism ;  it  is  merely  the  re- 
flection upon  the  way  in  which  we  have  attained,  or 
could  attain,  to  a  judgment,  the  conclusion;  no 
new  insight  is  ever  reached."^  The  two  opposed 
views  thus  indicated  do  not  necessitate  conflicting 
or  mutually  exclusive  processes.  It  is  better  to 
regard  them,  not  as  radically  different  types  of 
inference,  but  rather  as  different  phases  of  one  and 
the  same  inferential  process.  We  have  seen  that 
inference  consists  in  interpreting  the  implications 
of  the  system  to  which  the  given  in  consciousness 
belongs.  In  the  light  of  this  definition  we  can  best 
indicate  the  relative  functions  of  induction  and  de- 
duction in  the  process  of  inference.  When  the 
system  can  be  considered  as  a  Avhole,  and  is  appre- 
hended in  its  entirety,  then  it  may  become  the 
ground  upon  which  the  inference  is  based,  resulting 
in  unfolding  the  necessary  nature  or  relations  of 
any  of  the  parts  considered  in  themselves,  or  in 
reference  to  the  system  as  a  whole.  The  procedure 
in  such  a  case  is  from  the  nature  of  the  whole 
system,  to  the  nature  of  the  several  parts,  and  their 
existent  relations,  and  this  is  deductive  in  its  es- 
sential features. 

On  the  other  hand,  when  we  know  the  various 
parts,  and  proceed  from  them  as  data  to  construct 
the  system  which  their  known  nature  and  rela- 
tions necessitate,  it  is  induction,  or  procedure  from 
elementary  parts  to  the  whole  thus  necessitated. 
1  See  Ueberweg,  System  of  Logic,  etc.,  p.  345. 


18  INDUCXn^  LOGIC 

From  a  knowledge  of  the  planetary  system,  we 
can  infer  the  necessary  positions  of  sun,  moon,  and 
earth  at  any  required  time,  as,  for  instance,  in  the 
calculation  of  an  eclipse.  This  is  deduction.  But 
when  we  begin  with  investigating  the  several  move- 
ments of  the  different  planets,  and  from  them  infer 
the  necessary  nature  of  the  system  of  which  they 
are  parts,  we  have  the  process  of  induction.  Such 
processes  we  see  must  be  complementary,  and  mu- 
tually dependent.  As  Lavater  says,  "  He  only  sees 
well  who  sees  the  whole  in  the  parts,  and  the  parts 
in  the  wdiole." 

Moreover,  the  distinction  between  deduction  and 
induction  may  be  shown  through  their  respective 
relations  to  the  universal,  which  we  have  seen  is  the 
ground  of  inference.  The  question  whose  answer 
leads  to  the  deductive  process  in  reasoning,  is,  What 
does  the  universal  necessitate  ?  In  induction,  the 
question  which  starts  the  investigation  is.  Into 
what  system  may  I  construct  the  given  material 
properties  or  relations,  so  as  to  reach  a  universal 
concept  that  will  be  consistent  with  itself  and  with 
the  w^hole  of  knowledge  which  forms  the  world  of 
consciousness  ?  In  this  there  is  an  analytical  dis- 
crimination of  the  essential  and  accidental  elements, 
and  the  gathering  together  of  the  former  into  the 
complex  Avhole  wdiich  is  the  universal.  Induction, 
therefore,  is  inference  viewed  from  the  side  of  the 
differences ;  deduction  is  inference  viewed  from  that 
of  the  universal.  For  instance,  we  may  investigate 
the  characteristic  features  of  a  diamond,  and  find 
that  a  certain  specific  gravity,  3.53  as  compared  with 


INDUCTION  AND  DEDUCTION  19 

water,  is  a  constant  and  determining  attribute,  and 
as  sucli  must  be  incorporated  as  an  essential  element 
of  the  general  concept  diamond.  We  can  then  form 
the  universal  judgment.  Whatever  stones  possess 
this  specific  gravity  are  diamonds.  Their  differences, 
regarding  size,  brilliancy,  etc.,  may  all  be  set  aside 
as  accidental,  but  the  one  constant  determining 
feature  indicates  a  oneness  in  which  they  all  agree. 

And  so  with  the  other  essential  attributes.  After 
possessing  such  knowledge  gained  inductively,  we 
may  use  it  practically  in  a  deductive  manner; 
and  it  is  so  used  in  discriminating  between  true 
and  imitation  stones,  as  described  in  the  following 
process :  "  Diamonds,  rubies,  and  sapphires  are 
now  tested  by  floating  to  prove  their  genuineness. 
The  liquid  used  has  five  times  the  density  of  water, 
and  is  composed  of  double  nitrate  of  silver  and 
thallium.  The  tests  are  rapidly  made,  as  all  stones 
of  the  same  nature  have  the  same  specific  gravity, 
while  none  of  the  bogus  ones  have  the  same  weight 
as  those  they  are  made  to  imitate." 

Another  view  of  the  relation  of  induction  to  de- 
duction may  be  gained  by  calling  attention  to  the 
difference  of  significance  between  the  terms,  a  truth 
and  a  fact.  A  fact  carries  with  it  only  the  special 
and  individual  character  of  the  particular  occur- 
rence in  which  it  is  manifested.  A  truth,  however, 
is  always  universal  in  its  very  nature,  admitting  of 
universal  application,  and  ca^^able  of  illustration 
in  an  indefinite  number  of  different  facts  which 
embody  its  essence.  In  deduction  we  have  given 
some  truth  of  universal  nature  that  leads  to  indi- 


20  INDUCTIVE  LOGIC 

vidual  facts  that  may  be  subsumed  under  it.  In 
induction,  we  interpret  a  fact  or  a  number  of  facts 
in  the  light  of  their  universal  implication,  on 
the  ground  that  there  can  be  no  such  thing  as 
an  isolated  fact,  but  every  fact  must  have  some 
relation  to  a  universal  to  which  it  must  be  referred. 
While  considering  the  distinctions  between  in- 
duction and  deduction,  we  must  not  overlook  their 
mutual  dependence.  We  cannot  proceed  in  de- 
duction irrespective  of  induction,  because  the  uni- 
versal upon  Avhich  the  deductive  process  is  based 
arises  in  the  majority  of  cases  from  -a  previous 
induction.  It  is  true  that  the  universal  term  may 
be  in  a  proposition  that  is  known  a  priori,  as  the 
axioms  of  geometry  and  certain  space  and  time 
postulates ;  but  a  very  small  proportion  of  major 
premises  can  be  said  to  have  such  an  origin,  and 
their  resulting  conclusions  have  very  slight  ma- 
terial significance.  Deduction  thfit  reaches  other 
than  purely  abstract  and  formal  conclusions  must 
rest  upon  induction  for  the  material  to  form  its 
premises.  We  find  this  even  in  the  technical  con- 
struction of  the  syllogism,  where,  for  instance,  the 
question  of  the  distribution  of  the  terms  is  raised. 
We  may  insist  that  a  certain  middle  term  is  dis- 
tributed as  it  is  the  subject  of  an  universal  affirma- 
tive proposition ;  but  then  the  further  question 
naturally  suggests  itself.  How  do  we  know  that 
the  proposition  in  question  is  really  a  universal  ? 
Its  material  significance  alone  tells  us  that  we 
may  write  it  as  an  A  or  /  proposition,  as  the  case 
may  be.     The  matter  is  a  function  of  the   form, 


INDUCTION  AND  DEDUCTION  21 

and  the  form  a  function  of  the  matter.  They  can- 
not be  separated  in  fact,  unless  we  conceive  reason- 
ing as  a  purely  formal  process  of  determining  a 
conclusion,  irrespective  of  the  trnth  or  falsity  of 
the  premises.  If  we  regard  the  premises  as 
given,  and  we  accept  them  with  unquestioning 
credence,  the  deduction  is  purely  formal ;  so 
also  if  the  various  terms  are  expressed  by  letters 
A,  B,  C,  etc.,  and  devoid  of  any  material  signifi- 
cance. Any  process  of  reasoning  based  upon  a 
slavish  acceptance  of  premises  can  only  reach 
artificial  and  even  false  results.  In  the  actual  ex- 
periences of  life  onr  premises  are  not  made  for 
ns.  They  must  be  constructed  by  us  through  our 
interpretation  of  reality.  Disregard  of  this  has 
brought  formal  logic  into  much  disrepute,  and  it 
has  often  degenerated  into  the  barren  discussion  of 
logical  puzzles  and  quibbles.  Grant  a  person  any 
premises  he  may  choose  to  assume,  irrespective  of 
an  inductive  test  of  their  validity,  he  can  prove 
black  white,  and  white  black. 

On  the  other  hand,  induction  is  dependent  upon 
deduction;  for  we  cannot  reason  from  particular 
instances  to  a  universal  proposition,  unless  Ave  as- 
sume as  basis  of  the  whole  inductive  process  some 
postulate  which  has  real  universal  significance. 
Otherwise,  we  reach  only  a  high  degree  of  prob- 
ability, but  not  necessity;  a  rude  generalization, 
but  not  universality.  When  we  assert  some  such 
general  statement  as  this,  that  arsenic  always  acts 
as  a  poison,  we  have  the  universal  character  of  the 
proposition   upon  an  underlying  postulate  that  is 


22  INDUCTIVE  LOGIC 

understood  even  though  it  is  not  expressed,  such  as 
the  uniformity  of  nature,  tliat  under  identical  con- 
ditions we  always  look  for  identical  effects.  This 
will  be  discussed  later  more  in  detail ;  it  is  re- 
ferred to  at  this  point  merely  to  illustrate  the  de- 
ductive basis  of  induction.  Bradley  insists  that 
there  can  be  no  such  thing  as  induction,  because  it 
always  rests  upon  an  implied  universal  which  gives 
to  the  process  as  a  whole  a  deductive  character.^ 
His  criticism  has  the  force  only  of  proving  that 
induction  cannot  be  independent  of  deduction. 
This  dependence  does  not,  however,  necessarily 
vitiate  the  integrity  of  induction  as  a  mode  of  the 
inferential  process.  Lotze  has  placed  special  em- 
phasis upon  this  dependence  of  induction  upon 
deduction.  He  says :  "  It  is  the  custom  in  our 
day  to  collect  into  one  body  the  numerous  opera- 
tions which  assist  us  in  ascending  from  particulars 
to  generals,  or  to  call  this  inductive  logic,  and  to 
set  it  against  the  deductive  or  demonstrative  logic 
along  with  much  disparagement  of  the  latter.  Such 
disparagement  rests  on  a  mistake.  The  inductive 
methods,  it  is  certain,  are  the  most  effectual  helps 
to  the  attainment  of  new  truth,  but  it  is  no  less 
certain  that  they  rest  entirely  on  the  results  of 
deductive  logic."  - 

Moreover,  in  induction  the  results  obtained  and 
formulated  in  general  propositions  may  be  extended, 
and  often  modihed  by  a  deduction  which  is  based 

1  Bradley,  Principles  of  Logic,  p.  332. 

2  Lotze,  Logic,  p.  288.  See  also  Bosanquet,  Logic,  Vol.  II. 
p.  119. 


INDUCTION  AND  DEDUCTION  23 

upon  tliem  as  major  premises ;  for  the  deduction 
thus  proceeding  from  them  reveals  new  instances 
which  conform  or  perhaps  modify  the  simple  induc- 
tive results  themselves.  What  is  popularly  called 
a  hasty  generalization,  if  made  a  major  premise  of 
a  syllogism,  will  often  lead  us  astray  through  the 
deductions  drawn  from  it.  As  soon  as  we  are  aware 
of  this,  we  return  to  question  the  validity  of  the 
generalization,  whose  weakness  is  not  appreciated 
until  thus  tested  and  revealed.  Thus  deduction 
serves  to  extend  and  correct  the  results  of  induc- 
tion, and  at  the  same  time  it  itself  is  dependent 
upon  the  results  of  inductive  generalization  for  the 
material  to  form  its  premises.  We  come  to  see, 
therefore,  how  intimately  associated  these  two  proc- 
esses are  in  actual  reasoning.  For  convenience  of 
illustrating  their  individual  characteristics,  they 
may  be  considered  as  separate,  and  each  investigated 
as  an  independent  mode  of  inference.  But  they  are 
in  reality  mutually  related  and  dependent,  and  are 
always  found  manifesting  their  functions  together. 
In  any  course  of  reasoning  concerning  the  conduct 
of  our  every-day  affairs,  or  in  scientific  investigation, 
anywhere,  indeed,  outside  of  the  artificial  examples 
of  logical  text-books,  we  reason  both  inductively  and 
deductively  in  one  complex  process. 


CHAPTER   III 

The  Essentials  of  Ixductiox 

We  now  proceed  to  a  more  precise  determination 
of  the  nature  of  induction.  Its  point  of  view  in  all 
reasoning  regards  concrete  instances.  They  are  the 
data,  and  from  them  general  propositions  are  to 
result.  The  procedure  is  from  given  facts  to  laws 
which  are  the  ground  and  explanation  of  these 
facts.  We  are  here,  however,  at  once  struck  with  the 
evident  break  in  the  course  of  our  reasoning.  Pro- 
cedure from  the  particular  to  the  universal  cannot 
be  a  continuous  process.  There  is  a  gap  somewhere. 
The  conclusion  contains  more  than  the  premises. 
In  deduction,  Ave  are  proceeding  from  the  greater 
to  the  less,  and  we  experience  no  violation  of  our 
logical  sense  ;  but  at  once  we  appreciate  the  diffi- 
culty which  attends  the  reverse  process,  from  the 
less  to  the  greater.  Here  we  soon  reach  a  point 
where  we  pass  beyond  the  sphere  of  our  experience 
to  the  generalization  which  necessarily  embraces 
far  more  than  our  experience.  This  is  the  so-called 
inductive  leap ;  or  it  is  sometimes  referred  to  as  the 
inductive  hazard.  But  is  this  a  leap  in  the  dark 
—  a  wild  guess  concerning  all  that  lies  beyond  the 
sensuous  sphere  of  our  immediate  experience  ?  This 
24 


THE  ESSENTIALS   OF   INDUCTION  25 

would  be  the  case,  were  we  compelled  to  use  the 
mere  data  of  experience  as  sole  ground  for  our 
inferences.  John  Stuart  Mill  insists  that  nothing- 
whatever  is  given  in  consciousness  but  particular 
sensations,  and  these  are  but  subjective  states  of 
feeling,  and  with  no  assurance  of  any  definite  cor- 
respondence with  the  external  world.  With  such 
purely  empirical  data  it  is  impossible  to  proceed  to 
truths  of  universal  validity.  It  is  necessary  to  post- 
ulate some  universal  truth  which  the  mind  through 
strictly  a  priori  considerations  is  constrained  to 
formulate,  and  which  will  serve  to  bridge  the  gulf 
between  the  particular  and  the  universal. 

This  postulate  has  been  variously  expressed  by 
different  authors,  yet  with  substantially  the  same 
significance  in  all.  In  the  older  logic,  it  is  put 
under  the  convenient  formula  of  the  uniformity  of 
nature;  that  is,  that  beyond  the  sphere  of  experi- 
ence, phenomena  will  behave  in  the  same  manner, 
under  like  conditions,  as  in  the  sphere  of  immediate 
observation  and  experiment.  In  the  modern  logic 
this  is  somewhat  differently  expressed.  The  phrase 
''  uniformity  of  nature,"  being  somewhat  indefinite 
and  implying  a  point  of  view  purely  objective,  is 
not  used.  Modern  writers  have  omitted  it  largely 
from  their  terminology.  Lotze  says  :  "  The  logical 
idea  upon  which  induction  rests  is  by  no  means 
merely  probable,  but  certain  and  irrefragable.  It 
consists  in  the  conviction,  .based  upon  the  principle 
of  identity,  that  every  determinate  phenomenon  M 
can  depend  upon  only  one  determinate  condition, 
and  accordingly  that,  where  under  apparently  dif- 


26  INDUCTIVE   LOGIC 

ferent  circumstances  or  in  different  subjects  P,  S, 
T,  U,  the  same  3f  occurs,  there  must  inevitably  be 
in  them  some  common  element  %  which  is  the  true 
identical  condition  of  M,  or  the  true  subject  of  i^f."  ^ 
We  have  a  somewhat  similar  description  of  the 
basis  of  the  inductive  process  given  by  Sigwart: 
^'The  logical  justification  of  the  inductive  process 
rests  upon  the  fact  that  it  is  an  inevitable  postulate 
of  our  effort  after  knowledge  that  the  given  is 
necessary,  and  can  be  known  as  proceeding  from  its 
grounds  according  to  universal  laws."  ^  Bosanquet 
considers  as  the  basis  of  inductive  inference  that 
w^hich  he  calls  the  postulate  of  knowledge,  that  "  the 
universe  is  a  rational  system,  taking  rational  to  mean 
not  only  of  such  a  nature  that  it  can  be  known  by 
intelligence,  but  further  of  such  a  nature  that  it 
can  be  known  and  handled  by  our  intelligence."  ^ 

I  have  quoted  these  passages  from  Lotze,  Bosan- 
quet, and  Sigwart,  that  we  may  appreciate  the  mod- 
ern tendency  to  derive  the  inductive  postulate  from 
an  epistemological  source ;  namely,  that  our  knowl- 
edge must  be  consistent  throughout  Avith  itself, 
part  to  part,  and  parts  to  whole,  and  that  the  world 
for  us  is  the  world  as  constructed  by  our  knowledge. 
Whatever  is  given  in  consciousness  must  belong 
therefore  in  the  one  place  where  it  appropriately 
and  necessarily  belongs.  Here  also  there  must  be 
a  place  for  everything,  and  everything  in  its  place. 
There  must  be  a  uniformity  of  consciousness ;  that 

1  Lotze,  Lof/ic,  p.  102. 

2  Sigwart,  Logic  (Eng.  translation),  Vol.  II.  p.  289. 

3  Bosanquet,  The  Es:ientials  of  Logic,  p.  166. 


THE  ESSENTIALS  OF  INDUCTION  27 

is,  the  primary  postulate  and  the  uniformity  of 
nature  is  secondary  to  this,  and  implied  in  it.  This 
postulate  may  also  be  expressed  as  follows :  What 
is  once  true,  is  always  true.  Here  true  is  used  in 
the  sense  of  the  universal  significance  of  a  fact. 
Whenever  a  concrete  instance  is  joresent  in  con- 
sciousness, its  existence  must  be  considered  as 
necessitated  by  some  antecedent  which  can  satis- 
factorily account  for  it,  and  which  can  at  the  same 
time  be  appropriately  adjusted  to  the  whole  of  our 
knowledge  in  interpreting  it.  Bosanquet  says  that 
"ideally  speaking  every  concrete  real  totality  can 
be  analyzed  into  a  complex  of  necessary  relations."  ^ 
These  necessary  relations  of  course  have  a  universal 
significance,  and  therefore  in  every  concrete  in- 
stance, if  we  can  rightly  interpret  it,  we  may  dis- 
cern the  universal  element  which  is  contained  in  it, 
and  gives  it  a  place  and  meaning  in  the  world  as 
cognized  by  us. 

There  is  a  sense  in  which  induction  may  be  re- 
garded as  the  inverse  process  of  deduction.  In 
deduction  the  problem  is  concerned  with  the  ques- 
tion. What  does  the  universal  necessitate  ?  In 
induction,  the  instance  is  given,  and  the  problem 
is.  What  universal  can  be  discovered  which  could 
give  rise  to  the  instance  in  question  ?  This  view 
of  induction  is  especially  associated  with  the  name 
of  Jevons,  whose  inductive  system  is  described  as 
the  inverse  of  deduction.  He  calls  it  the  decipher- 
ing of  the  hidden  meaning  of  natural  phenomena.^ 

1  Bosanquet,  Logic,  Vol.  II.  p.  82. 

2  Jevons,  Principles  of  Science,  p.  124. 


28  INDUCTIVE  LOGIC 

The  name  commonly  used  to  designate  this  view  of 
induction  is  that  of  "  reduction,"  originally  sug- 
gested by  Duhamel.^  This  process  was  known  to 
the  old  logicians,  who  called  it  "  Method  "  to  denpte 
the  process  of  hunting  for  middle  terms  by  the  aid 
of  which  a  given  conclusion  could  be  proved.^  Like 
all  inverse  processes,  it  is  by  itself  an  indeterminate 

one. 

Given  All  A  is  B,  and 

All  B  is  C, 
we  infer  by  the  direct  process  of  deduction  that 

All  A  is  a 

But  in  the  indirect  or  inverse  process  we  have 
given  all  A  is  C,  and  the  problem,  to  find  a  middle 
term  which  necessitates  such  a  conclusion,  is  an 
indeterminate  one.  There  may  be  a  number  of 
middle  terms.  This  is  analogous  to  the  method 
of  integral  calculus ;  while  differentiation  leads  to 
a  definite  result,  the  inverse  process  of  integration 
leads  to  an  indeterminate  result.  So  also  we  mul- 
tiply two  numbers,  producing  one  determinate  re- 
sult ;  but  inversely,  when  we  have  given  a  certain 
number,  and  ask  what  factors  multii)lied  together 
con  Id  produce  this  number,  we  may  reach  several 
different  solutions.  The  answer  is  indeterminate. 
Professor  Jevons,  in  his  scheme  of  inductive  infer- 
ence, falls  back  upon  probability  to  indicate  which 
of  several  possibilities  is  the  most  likely  one  in  the 

1  Duharael,  Methodes,  Vol.  I.  p.  24. 

2  Veun,  Empirical  Logic,  p.  3G1. 


THE  ESSENTIALS  OF  INDUCTION  29 

given  case.^  But  before  the  inverse  operation  can  re- 
sult in  determinate  results,  the  given  terms  such  as 
A  and  (7  must  be  subjected  to  some  analysis  in  order 
that  their  material  signification  may  give  sugges- 
tion as  to  the  nature  of  the  middle  term.  For  in- 
stance, a  man  is  found  dead,  washed  ashore  by  the 
tide ;  the  natural  supposition  would  be  that  he  met 
his  death  by  drowning.  And  yet  it  might  possibly 
happen  that  the  man  died  through  injuries  inflicted 
by  blows,  or  by  poison,  or  heart  failure.  The  at- 
tendant circumstances  and  bodily  indications  must 
suggest  the  most  probable  cause  to  account  for  the 
given  effect.  Venn  criticises  Jevons'  view  of  induc- 
tion, making  it  the  inverse  process  of  deduction,  on 
the  ground  that  it  is  purely  a  formal  process,  and 
therefore  can  lead  only  to  indeterminate  results.^ 

It  is  always  possible,  however,  to  make  some 
analysis  of  the  material  significance  of  the  data,  as 
has  been  above  indicated,  which  relieves  the  purely 
formal  processes  from  the  indefiniteness  of  the  re- 
sults. Bosanquet  criticises  Jevons'  theory  of  in- 
ductive inference,  in  that  the  hypothesis  proposed 
to  account  for  the  given  in  reality  can  at  best  be 
only  highly  probable.^  However,  Venn,  Lotze,  Bo- 
sanquet, Sigwart,  all  allow  a  place  to  the  inverse 
function  of  all  inductive  reasoning;  their  conten- 
tion, however,  is  this,  that  it  does  not  furnish  an 
adequate  account  of  the  whole  matter.** 

1  Jevons,  Principles  of  Science,  p.  219. 

2  Empirical  Logic,  p.  359. 

3  Bosanquet,  Logic,  Vol.  II.  p.  175. 

4  Venn,  361;  Bosanquet,  Vol.  II.  p.  175;  Sigwart,  Vol.  II. 
p.  203,  289.     Lotze,  Outlines  of  Logic,  p.  93. 


30  INDUCTIVE  LOGIC 

It  is  interesting  to  note  that  AVhewell's  theory  of 
induction  corresponds  in  the  main  to  this  idea  of 
reduction,  or  inverse  process.  He  finds  in  induc- 
tion a  twofohl  operation  of  the  mind,  consisting  in 
the  colligation  of  facts  and  the  explication  of  con- 
ceptions. By  the  colligation  of  facts  he  refers  to 
that  insight  which  is  able  to  see  the  connections 
and  relations  which  necessarily  exist  between  the 
different  phenomena  present  in  consciousness ;  and 
by  explication  of  conceptions  he  refers  to  the  ap- 
propriate fitting  in  of  these  related  facts  to  some 
conception  of  the  mind  which  most  readily  ac- 
counts for  them.-^  Such  a  process  is  merely  the 
reading  of  given  facts  backward  to  their  origin, 
or  substantially  an  inverse  process,  where  the  pro- 
cedure is  from  the  given  concrete  to  the  explanation 
of  the  same  in  terms  of  the  universal  to  which  it 
can  be  most  appropriately  referred.  So  also  Mill's 
account  of  procedure  by  hypothesis,  as  we  shall  see 
later  on,  presents  characteristics  similar  to  this 
process  of  reduction. 

The  end  of  induction  is  to  discover  a  law  having 
objective  validity  and  universal  application.  There 
is  a  distinction  which  must  be  noticed  and  clearly 
kept  in  mind ;  namely,  the  distinction  between  a  law 
and  a  rule.  Induction  seeks  a  law,  and  not  a  rule. 
A  law  expresses  the  essential  and  universal  rela- 
tions subsisting  between  given  phenomena,  elimi- 
nating entirely  all  accidental  and  local  coloring.  A 
law  has  objective  validity,  and  preserves  a  constant 
nature.     There  can  be  only  one  law  in  reference 

1  Whewell,  Philosophy  of  the  Inductive  ScienceSy  pp.  172, 202. 


THE  ESSENTIALS  OF  INDUCTION  31 

to  one  and  the  same  connection  of  facts.  A  rule, 
however,  is  subjective,  dealing  with  the  individual's 
attitude  to  phenomena,  rather  than  an  explanation 
of  the  essential  features  of  the  phenomena  them- 
selves. It  often  is  determined  in  the  concrete  by 
that  which  is  external,  local,  and  accidental.  There 
may  be  many  rules,  varying  with  many  minds  and 
many  climes.  Fundamental  and  universal  laws  of 
political  economy  become  maxims  and  rules  in  dif- 
ferent communities.  The  laws  of  morality,  univer- 
sal and  immutable,  become  rules  of  conduct  in  in- 
dividual experience  admitting  of  wide  difference  of 
opinion  and  diversity  of  application.^  In  the  proc- 
esses of  induction,  therefore,  the  law  is  the  desidera- 
tum, and  not  the  rule. 

Law,  however,  is  used  rather  loosely  in  our  ordi- 
nary terminology.  Law  as  used  in  jurisprudence 
has  a  meaning  quite  different  from  law  as  used  in 
physical  science.  And  so,  also,  the  laws  of  biology, 
the  laws  of  political  economy,  the  laws  of  ethics, 
are  referred  to  with  different  shades  of  meaning  in 
each  sphere.  However  ambiguous  may  be  the  sig- 
nificance of  "  law  "  in  ordinary  thought  and  usage, 
nevertheless  in  induction  it  has  a  constant  and  a 
simple  significance,  which  if  carefully  adhered  to 
will  avoid  confusion,  and  obscurity  as  well,  in  our 
inferential  processes  and  results.  Law  in  induction 
is  always  in  the  form  of  an  hypothetical  universal :  — 

If  A  is,  B  is. 

It  does  not  assert  what  has  happened,  but  .what 
1  Lotze,  Logic,  p.  335. 


32  INDUCTIVE  LOGIC 

should  happen  under  certain  conditions.  Given 
the  antecedent  A,  a  certain  determinate  consequent 
B  is  always  necessitated.  The  relation  is  constant 
and  invariable,  and  therefore  has  a  universal  signifi- 
cance. 

Induction  holds  a  peculiar  and  important  place 
in  our  every-day  life,  because  it  has  to  do  with  the 
analytical  treatment  of  instances  as  they  appear  in 
experience.  The  large  part  of  our  conscious  think- 
ing has  to  do  with  the  concrete,  the  raw  material 
of  experience ;  this,  induction  alone  can  handle. 
Leonardo  da  Vinci's  maxim  was  "  to  begin  with  ex- 
l^erience  and  by  means  of  it  to  direct  the  reason."  ^ 
Thus  the  superstructure  of  knowledge  is  raised  day 
by  day.  The  given  is  continually  being  interpreted 
and  referred  to  its  appropriate  place,  as  the  stones 
of  the  quarry  are  hewn  and  fitted  in  their  proper 
position  in  the  building  for  which  they  have  been 
designed.  There  are  certain  individual  experiences 
which  it  is  impossible  to  determine  through  our 
syllogistic  forms.  They  cannot  be  judged  deduc- 
tively. There  is  no  general  category  under  which 
they  can  be  subsumed.  They  may  be  formally 
illogical  if  thus  expressed,  and  yet  admit  of  direct 
investigation  and  experiment  in  an  inductive  man- 
ner, for  the  purpose  of  disclosing  the  law  under- 
lying them  and  as  yet  unknown. 

It  often   happens   that   through   indifference  or 

indolence,  we  are  content  to  refer  many  phenomena 

to  long-established  and  convenient  categories,  which, 

if  investigated  independently,  we  would  find  could 

1  Ueberweg,  Logic,  p.  42. 


THE  ESSENTIALS   OF  INDUCTION  33 

not  possibly  be  so  treated.  The  convenient  pigeon 
hole,  because  near  at  hand,  receives  much  that  does 
not  properly  belong  there.  It  is  the  office  of  induc- 
tion to  investigate  anew  the  old  material,  and  then 
to  reclassify  in  accordance  with  the  revised  gen- 
eralizations which  such  investigations  may  neces- 
sitate. 

The  procedure  by  induction  is  in  keeping  with 
the  scientific  spirit  of  the  day,  —  to  interpret  the 
phenomena  of  nature  as  given,  and  not  to  antici- 
pate nature  through  preconceptions,  and  wrest  fact 
in  order  to  fit  theory.  It  comes  to  the  sources  in 
nature  with  empty  vessels  to  draw  and  carry  away 
that  which  nature  alone  can  give. 


CHAPTER   IV 

Types  of  Ixductive  Inference 

The  process  of  induction,  as  we  have  seen,  is  a 
procedure  from  given  instances  to  the  discovery  of 
the  law  which  underlies  them,  and  which  is  the 
ground  of  the  connection  of  the  various  attributes 
and  relations  that  unite  in  the  one  concrete  whole. 
Viewed  from  the  standpoint  of  the  direction  of  the 
process,  we  have  found  that  it  is  always  towards 
some  general  expression  of  individual  experiences, 
and  in  this  respect  it  is  the  inverse  of  deduction, 
which  proceeds  from  the  general  to  the  particular 
which  is  embraced  in  it.  There  is,  however,  another 
and  important  point  of  view  that  should  not  be  over- 
looked. We  have  to  consider  the  mode  of  the  proc- 
ess as  well  as  its  direction ;  not  merely  the  result 
to  be  attained,  but  also  the  peculiar  manner  of 
realizing  the  same  must  be  considered.  Difference 
in  method  here  gives  rise  to  various  kinds  of  induc- 
tive inference.  The  end  proposed  in  all  is  to  gen- 
eralize our  experiences  as  they  occur  in  the  concrete 
and  particular.  When  I  find  a  given  phenomenon, 
A,  given  in  consciousness,  and  characterized  by 
several  distinctive  features  among  which  I  note 
si)ecially  the  mark  B,  the  question  at  once  most 
34 


TYPES  OF  INDUCTIVE  INFERENCE  35 

naturally  suggests  itself  Is  there  a  reasonable 
expectation  that  I  shall  always  find  B  as  an  insep- 
arable accompaniment  of  A,  so  that  I  can  assert 
confidently  that  whenever  A  is  found,  B  also  will 
be  found?  There  are  three  ways  of  satisfying 
ourselves  as  to  the  existence  of  any  constant  rather 
than  coincidental  connection  between  antecedent 
and  consequent,  as  A  and  B.  These  give  rise  to 
three  different  methods  of  inductive  research,  and 
they  are  as  follows :  — 

I.    The  Method  of  Enumeration. 
II.    The  Method  of  Comparison,  or  Analogy. 

III.  The  Method  of  Scientific  Analysis,  or 
Search   after   Causal    Connection. 

Failure  to  distinguish  between  the  three  methods 
has  given  rise  to  confusion  in  the  definition  of  and 
corresponding  reference  to  inductive  inference ; 
some  authors  use  induction  in  one,  and  some  in 
another  of  these  senses.  It  is  necessary  to  dis- 
criminate carefully,  and  to  maintain  a  strict  con- 
sistency in  the  usage  of  the  terms  as  defined. 

I.  The  Method  of  Enumeration.  —  We  observe  the 
various  instances  in  which  certain  attributes,  as  A 
and  B,  are  conjoined  in  our  experience.  We  count 
them  in  the  sense  of  noting  to  what  extent  they 
accumulate,  without  noticing  any  exception  to  what 
seems  at  least  an  invariable  connection.  AVe  do 
not  necessarily  count  by  precise  enumeration  reach- 
ing a  numerically  definite  result.  We  notice 
merely  to  what  extent  the  observed  instances  of 
like  nature  accumulate;  that  is,  whether  a  few,  a 
considerable  number,  or  a  very  large  number.     The 


36  INDUCTIVE  LOGIC 

mere  number  of  instances  produces  a  certain  psycho- 
logical impression,  whatever  may  be  their  logical 
force.  This  is  brought  about  through  the  laws  of 
association,  and  creates  an  expectation  of  a  con- 
tinuous repetition  of  the  experience  in  question. 
This  arises  from  a  natural  tendency  of  the  mind  to 
generalize.  We  observe  that  crows  are  black ;  and 
the  increasing  number  of  confirming  instances  goes 
far  to  establish  a  connection  between  the  crow  and 
its  color  which  seems  to  have  universal  validity. 
The  enumeration  of  instances  may  lead  us  to  any 
one  of  three  results  :  — 

1.  We  may  meet  with  no  exception  whatsoever, 
until  the  scope  of  observation  completely  embraces 
the  sum  of  all  possible  instances.  This  is  complete 
enumeration,  and  when  enumeration  reaches  this 
limit,  it  passes  over  into  deductive  reasoning,  by 
virtue  of  the  logical  canon  that  whatever  is  true  of 
the  parts  is  true  of  the  whole  distributively  ^  that  is, 
provided  the  summation  of  the  parts  has  been  an 
exhaustive  one.  We  assert  that  all  the  sheep  of  a 
given  flock  are  white ;  for  we  have  observed  each 
separately  and  no  one  has  been  missed  in  the  count. 
So,  also,  the  judgment  that  all  planets  move  around 
the  sun,  resulting  from  an  enumeration  of  the  planets 
one  by  one.  It  is  possible  also  to  have  a  perfect  in- 
duction with  an  infinite  enumeration  of  parts.  This 
is  possible  in  two  cases,  as  pointed  out  by  Beneke.' 
First,  when  the  parts  are  connected  together  contin- 
uously in  space,  so  that  a  survey  of  all  is  possible 
in  a  finite,  and  often  a  very  short  time.  This  occurs 
1  Quoted  by  Ueberweg,  Logic,  p.  482, 


TYPES   OF  INDUCTIVE  INFERENCE  37 

in  geometrical  demonstration  when  the  inference, 
based  upon  the  simple  figure  it  refers  to,  is  extended 
to  all  figures  falling  under  the  like  definition.  And 
second,  when  the  parts  are  not  continuously  con- 
nected, if  it  can  be  proved  syllogistically  that  what 
is  true  of  a  definite  nth  part,  must  also  be  true  for 
the  (71  4-  l)th  part. 

Perfect  induction  also  embraces  arithmetical 
method  and  computation.  Here  the  whole,  which 
is  the  sum  of  the  facts  in  each  case,  is  a  totality 
or  universal  whose  differences,  which  are  all  sepa- 
rate and  distinguishable,  are  yet  homogeneous  and 
equal.^  There  is  no  qualitative  differentiation  of 
parts,  only  a  quantitative  one.  The  total  is  the 
sum  of  the  units,  and  each  unit  is  like  every  other 
one.  If  we  have  one  hundred  units  making  a 
totality,  the  one  that  may  be  the  twenty-seventh 
is  precisely  like  the  sixty-seventh.  It  is  a  case 
where  each  one  counts  for  one,  and  no  one  for 
more  than  one  in  an  absolutely  literal  sense. 

It  has  been  urged  against  perfect  induction  that 
it  affords  no  new  information,  and,  therefore,  its 
results  are  not  valuable.  However,  the  summation 
of  particulars  in  abbreviated  forms  is  always  an 
advantage.  It  is  a  labor-saving  process  to  the  mind. 
It  enables  the  mind  to  retain  a  large  number  of 
facts  by  throwing  them  into  one  and  the  same  cate- 
gory ;  and  it  facilitates  arithmetical  processes  by 
convenient  comprehending  of  units  within  a  totality. 

2.  The  second  result  that  is  possible,  is  that,  in 
counting  instances,  our  enumeration  should  prove 
1  Bosanquet,  Logic,  Vol.  II.  p.  54. 


38  INDUCTIVE  LOGIC 

incomplete.  From  the  necessities  of  the  case,  we 
are  often  not  able  to  observe  the  entire  sphere  of 
possible  occurrences  and  cover  the  whole  ground. 
It  may  be  that  beyond  the  sphere  of  our  expe- 
rience, the  constant  connection  between  certain 
phenomena  may  be  disturbed  by  the  appearance 
of  some  variable  factor  of  which  we  have  been 
wholly  ignorant.  It  is  the  possibilities  beyond 
the  sphere  of  observation  which  render  uncertain 
the  results  of  our  count.  We  are  sure  as  far  as  we 
have  observed ;  but  we  have  not  gone  far  enough 
perhaps.  Such  results,  formulated  in  general  prop- 
ositions, are  termed  empirical  laws ;  that  is,  gen- 
eralizations from  an  experience  necessarily  limited. 
3.  We  have  still  a  third  case ;  where  in  our 
enumeration  of  positive  instances  we  meet  with 
exceptions  to  a  greater  or  less  extent.  Here  we 
cannot  even  sum  up  the  actual  experience  in  terms 
of  a  generalization.  There  are  outstanding  excep- 
tions which  will  invalidate  it.  We  must,  therefore, 
fall  back  upon  the  theory  of  probability  and  the 
calculation  of  chances,  presuming  that,  in  general, 
we  will  meet  with  the  same  proportion  of  excep- 
tions to  positive  instances  in  the  future,  that  we 
have  already  observed  in  the  past.  So  we  make, 
in  our  minds  at  least,  comparative  tables  of  posi- 
tive cases  over  against  exceptions,  and  reach  a 
summary  of  the  result  in  the  form  of  a  ratio, 
whose  numerator  will  be  the  number  of  positive 
cases  observed,  and  the  denominator  the  total  num- 
ber of  instances  including  positive  instances  and 
the    corresponding   exceptions.     We   observe   that 


TYPES   OF  INDUCTIVE  INFERENCE  39 

some  cryptogamous  plants  possess  a  purely  cel- 
lular structure ;  others,  however,  do  not,  being 
partially  vascular.  The  probability  that  a  new 
cryptogam  will  be  cellular  can  be  estimated  only 
on  the  ground  of  the  comparative  number  of 
known  cryptogams  Avhich  are  cellular,  as  over 
against  the  total  number  of  cryptogams,  both  cel- 
lular and  vascular,  previously  observed.^ 

II.  The  Method  of  Analogy.  —  Here,  also,  we 
start  with  the  experience  that  A  is  characterized 
by  the  mark  B.  But  there  is  additional  knoAvledge 
of  which  we  may  avail  ourselves  in  the  generaliza- 
tion of  some  past  experience  already  effected,  such 
as  the  f  olloAving :  that  A  very  closely  resembles  C,  in 
that  the  two  have  many  properties  or  attributes  in 
common.  The  inference  by  analogy  is  that  C  also,  as 
well  as  A,  will  have  the  mark  B.  It  may  be  that  we 
cannot  examine  C  in  a  number  of  various  instances 
to  see  in  how  many  the  mark  B  occurs.  Our  only 
resource  is  the  inference  which  is  based  upon  the 
known  resemblances,  or  analogies.  This  kind  of 
inference,  for  example,  was  employed  by  Sir  Isaac 
Newton  in  a  very  interesting  manner.  He  had  ob- 
served that  certain  "fat,  sulphureous,  imctious 
bodies,"  such  as  camphor,  oils,  spirit  of  turpentine, 
amber,  etc.,  have  refractive  powers  two  or  three 
times  greater  than  might  be  anticipated  from  their 
densities.  He  noticed  also  the  unusually  high  re- 
fractive index  of  diamond,  and  from  this  resem- 
blance, based  upon  similarity  in  reference  to  one 
attribute  only,  he  inferred  that  diamond  also  would 

1  Jevons,  Principles  of  Science^  pp.  146,  147. 


40  INDUCTIVE  LOGIC 

prove  to  be  combustible.  His  prediction  in  this 
regard  was  verified  by  the  Florentine  Academicians 
in  1694.^  Brewster  made  a  striking  comment  upon 
Newton's  inference,  to  the  effect  that  if  Newton 
had  drawn  a  like  analogy  in  reference  to  greenock- 
ite  and  octahedrite  as  he  did  concerning  diamond, 
inasmuch  as  they,  too,  have  a  very  high  refractive 
index,  he  would  have  been  wholly  incorrect.  This 
is  an  indication  of  the  fact  that  argument  by  anal- 
ogy is  not  conclusive. 

Bosanquet  has  very  strikingly  expressed  the  es- 
sence of  the  analogical  method  in  saying  that  "  in 
Analogy  we  weigh  the  instances  rather  than  count 
them."  ^  The  distinction  between  analogy  and 
enumeration  of  instances  lies  in  this,  that  in  the 
former  we  count  similar  attributes  in  the  contents 
of  two  instances,  and  balance  them  against  the  dis- 
similar or  unknown.  In  induction  by  enumera- 
tion we  count  similar  instances,  considering  them 
in  their  totality  without  examination  and  compari- 
son of  their  respective  attributes. 

III.  The  Method  of  Scientific  Analysis.  —  The 
instance  in  question,  A,  which  is  characterized  by 
the  mark  B,  is  subjected  to  a  vigorous  analytical 
examination,  to  show  that  A  and  B  are  related 
through  a  causal  connection.  This  analysis  is 
effected  either  through  a  minute  observation  or 
by  means  of  exact  experiment.  The  end  to  be 
attained  by  such  analysis  is  to  separate  a  complex 
phenomenon   into  its   several   elements,  by  which 

1  Jevons,  Principles  of  Science,  p.  527. 

■-2  Bosauquet,  27te  Essentials  of  Logic,  p.  155. 


TYPES  OF   INDUCTIVE   INFERENCE  41 

process  a  causal  connection  may  be  revealed,  whose 
very  existence  is  disguised  by  the  complexity  of 
the  phenomenon.  For  instance,  the  phenomenon 
of  death  following  the  taking  of  arsenic  is  an 
event  so  complex  as  to  evade  a  precise  determina- 
tion of  the  causal  relation.  When  analyzed  into 
simpler  elements,  it  is  found  that  the  immediate 
effect  of  arsenic  upon  the  bodily  tissues  is  to 
harden  them  so  as  to  prevent  their  normal  function- 
ing. This  is  the  causal  ground  of  the  death  due  to 
arsenic.  Moreover,  this  analytic  process,  which 
may  be  appropriately  called  a  material  one,  is  sup- 
plemented by  a  formal  process  of  negation,  that  is, 
an  instance  in  which  the  suspected  causal  element 
is  absent  in  the  complex  phenomenon  under  in- 
vestigation, and  the  related  effect,  before  observed, 
now  no  longer  appears.  This  formal  process  acts 
as  a  check,  and  as  a  verification  as  well,  of  the 
material  analysis  of  the  phenomenon.  For  ex- 
ample, an  antidote,  as  sesquioxide  of  iron,  being 
administered,  no  death  from  arsenic  occurs ;  and  it 
is  also  observed  that  no  hardening  of  the  tissues 
has  resulted,  therefore  the  former  result,  hardening 
of  tissues  producing  death,  has  been  thus  corrobo- 
rated negatively  by  the  fact  that  where  no  harden- 
ing of  tissues  has  resulted,  death  does  not  follow. 

We  see  at  once  the  advantage  of  such  a  method 
over  that  of  counting  all  instances  where  taking  of 
arsenic  has  caused  death.  The  latter  is  a  phenom- 
enally adjudged  result ;  the  former  penetrates  with 
analytic  insight  to  the  ground  of  the  phenome- 
non itself.     Thus  one  instance,  if  its  parts  and  their 


42  INDUCTIVE  LOGIC 

manifold  relations  are  adequately  comprehended, 
may  suffice  for  a  universal  conclusion  based  upon  it. 
It  is  true,  however,  as  remarked  by  Bosanquet,  that 
"  number  of  observations  does,  as  a  rule,  assist  analy- 
sis and  contribute  to  eliminating  error.  Scientific 
analysis  as  such,  however,  does  not  deal  with  in- 
stances, but  only  with  contents."  ^ 

In  cases  where  the  phenomenon  does  not  reveal 
its  component  elements  under  observation,  and  it  is 
impossible  to  subject  it  to  experiment,  the  most 
likely  cause  of  the  effect  in  question  is  tentatively 
judged  to  be  the  real  cause,  until  it  can  be  verified 
in  reality.  This  is  procedure  by  hypothesis,  and 
is  always  resorted  to  as  preliminary  to  a  subsequent 
experiment  which  is  its  test,  or  else  in  lieu  of  such 
an  experiment  when  it  is  by  the  nature  of  the  case 
precluded.  It  is  a  form  of  ideal  analysis.  The  ex- 
periment is  constructed  mentally.  The  phenome- 
non is  separated  into  what  we  would  reasonably 
imagine  its  simpler  elements  would  be.  We  are 
constrained  to  believe  that  if  the  hypothetical  ante- 
cedent existed,  it  would  be  adequate  to  produce  the 
effect.  Although  rising  in  the  sphere  of  the  imagi- 
nation, it  is  that  with  which  the  mind  is,  for  the  time 
at  least,  satisfied  as  an  explanation  of  the  facts  which 
demand  some  cause  to  account  for  them.  Regard- 
ing induction  as  a  process  of  reduction,  hypothe- 
sis is  the  assumed  universal,  or  middle  term,  which 
will  necessitate  the  phenomenon  under  investiga- 
tion as  its  logical  conclusion. 

We  will  now  proceed  to  a  further  examination 

1  Bosauquet,  Lo(jic,  Vol.  II.  p.  118. 


TYPES   OF  INDUC  riVE   INFERENCE  43 

of   these  methods,  considered  both  singly  and  to- 
gether. 

1.  They  all  proceed  upon  the  supposition  that 
what  is  given  in  consciousness  has  some  necessary 
ground  for  its  being.  In  enumerative  induction, 
there  is  some  causal  connection  presupposed,  yet  in 
a  very  general  and  indefinite  manner,  and  accom- 
panied by  no  analysis  of  the  various  concepts  either 
by  a  systematic  observation  or  experiment.  It  is  a 
vague  sense  of  uniformity  which,  when  observed  for 
many  times,  we  feel  will  continue  indefinitely.  That 
which  has  happened  often  and  not  contradicted  car- 
ries with  it  a  certain  convincing  power  by  dint  of  bare 
repetition,  especially  to  persons  of  narrow  experi- 
ence, and  unaccustomed  to  discriminating  observa- 
tion. Ueberweg  has  made  the  following  comment  in 
reference  to  the  so-called  imperfect  induction.  "  The 
conclusion  is  made  universal  with  more  or  less  prob- 
ability, and  the  blank  which  remains  over  in  the 
given  relations  of  spheres  is  legitimately  filled  up 
partly  on  the  universal  presupposition  of  a  causal- 
nexus  in  the  objects  of  knowledge,  partly  on  the 
particular  presupposition  that  in  the  case  presented 
such  a  causal-nexus  exists  as  connects  the  subject 
and  predicate  of  the  conclusion.  The  degree  of  prob- 
ability of  the  inductive  inference  depends  in  each 
case  on  the  admissibility  of  this  last  presupposition, 
and  the  various  inductive  operations,  the  extension 
of  the  sphere  of  observation,  the  simplification  of  the 
observed  conditions  by  successive  exhaustion  of  the 
unessential,  etc.,  all  tend  to  secure  its  admissibility."^ 
1  Ueberweg,  Logic,  pp.  483  f . 


44  INDUCTIVE  LOGIC 

Analogy  likewise  proceeds  upon  the  assumption  of 
an  underlying  cause  among  the  observed  phenomena, 
and  this  is  more  definitely  in  the  foreground  through- 
out the  process  than  in  that  of  induction  by  enumer- 
ation. Analogy  is  based  upon  the  postulate  that  sim- 
ilar phenomena  have  similar  causes  ;  the  greater  the 
agreement  of  the  various  attributes  of  the  different 
phenomena  compared,  the  greater  will  be  the  result- 
ant probability  that  causes  capable  of  producing 
them  as  effects  will  be  similar.  The  similarity  of 
the  lightning  flash  to  the  electric  spark  suggested 
to  Benjamin  Franklin  the  possibility  that  they  were 
due  to  a  like  origin,  and  by  experiment  his  analogical 
reasoning  was  actually  confirmed,  as  is  well  known. 
Upon  the  theory  that  the  world  as  it  exists  for  us 
in  knowledge  forms  a  system  to  some  place  in  which 
every  phenomenon  given  in  experience  must  be 
appropriately  and  necessarily  referred,  it  follows, 
therefore,  that  a  simple  experience,  devoid  of  any 
complexity  of  parts,  may  fit  into  several  possible 
places  in  our  world  of  consciousness,  and  remain  so 
far  forth  indeterminate.  However,  a  complex  phe- 
nomenon, w4th  many  parts  intricately  connected, 
will  fit  into  one  unique  place  only  in  the  system  to 
which  it  must  be  referred.  It  is  like  a  key  that 
will  fit  into  only  one  lock.  The  presumption,  there- 
fore, is  that  any  other  phenomenon  which  resem- 
bles the  first  through  much  of  its  entire  content, 
part  for  part,  attribute  for  attribute,  Avill  also  re- 
semble it  further  as  regards  other  attributes  not  yet 
examined,  so  as  it  will  likewise  fit  into  the  peculiar 
place  in  the  system  of   knowledge  to  which  the 


TYPES  OF  INDUCTIVE  INFERENCE       45 

first  has  been  found  to  belong.  There  is  always  a 
strong  probability  that  agreement  in  spheres  of  great 
complexity  is  not  a  mere  coincidence,  but  the  result 
of  a  causal  relation.  One  characteristic  of  a  system, 
which  we  have  found  to  be  the  ground  of  inference 
generally,  is  the  co-ordination  of  like  things  under 
one  concept.  Analogy,  therefore,  is  based  upon  the 
view  of  causal  connections  within  the  system  which 
comprises  the  world  as  given  in  consciousness. 

In  the  third  method,  the  causal  relation  is  more 
prominent  still,  and  the  search  for  it  characterizes 
the  procedure  employed.  That,  which  in  the  other 
methods  may  exist  merely  as  a  vague  impression, 
is  here  formulated  and  made  the  direct  and  sole 
object  of  research. 

2.  The  three  methods  in  the  order  here  presented 
show  an  increasing  prominence  given  to  the  causal 
connection  in  the  phenomena  of  experience.  And 
therefore  they  possess  a  relatively  increasing  scien- 
tific value.  As  the  first  has  only  indirect  reference 
to  the  causal  connection  of  its  facts,  it  is  the  least 
trustworthy  and  has  no  claim  as  a  scientific  method. 
It  breaks  down  as  soon  as  an  exception  is  noted ; 
and  is  even  weakened  by  the  fact  that  it  is  con- 
stantly menaced  by  the  possibility  at  least  of  the 
appearance  of  an  exception.  "  How  do  we  know," 
says  Green,  "  that  the  instances,  with  the  examina- 
tion of  which  we  are  always  dispensing  on  the 
strength  of  the  rule  (that  is,  our  generalization), 
might  not  be  just  what  would  invalidate  it,  if  they 
were  examined  ?  "  ^  We  may  arrive  at  the  conclu- 
1  Green,  Phil.  Works,  Vol.  II.  p.  282. 


46  INDUCTIVE  LOGIC 

sion,  based  upon  our  observation  and  consequent 
record,  that  all  sheep  are  white,  and  yet  black 
sheep  do  occur,  even  in  every  flock,  as  the  proverb 
has  it.  According  to  Aristotle,  the  proposition  that 
all  swans  are  white,  was  a  perfectly  general  one, 
and  yet  in  recent  times  black  swans  have  been 
discovered  in  Australia.  Bacon's  criticism  upon 
this  method  has  become  classic  :  "  Inductio  quae 
procedit  per  enumerationem  simplicem,  res  puerilis 
est  et  precario  concludit  et  periculo  exponitur  ab 
instantia  contradictoria  et  plerumque  secundum 
pauciora  quam  par  est  et  exiis  tantummodo  quae 
presto  sunt  pronunciat."  ^ 

The  validity  of  this  method  of  procedure  depends 
largely  upon  the  probability  of  our  meeting  and 
noticing  exceptions  were  they  to  occur.  As  Lotze 
puts  it:  "A  man  who  never  observes  a  place  of 
public  resort  but  once  in  every  seven  days,  and  that 
on  a  Sunday  afternoon,  has  no  right  to  suppose, 
because  it  is  crowded  then,  that  it  is  as  crowded 
on  a  week-day."  ^  He  is  here  in  no  position  to  note 
the  exceptions  even  should  they  occur. 

Analogy,  unless  confirmed  by  experiment,  or  upon 
the  ground  of  resemblance  established  by  a  verifiable 
hypothesis,  has  no  claim  to  be  considered  as  a  scien- 
tific method.  There  may  be  false  analogies  depend- 
ing upon  surface  resemblances.  A  child  might 
conclude  that  oil  would  put  out  fire  because  it 
so  closely  resembles  water,  which  he  knows  can  ex- 
tinguish the  flames.  The  difference  between  essen- 
tial and  accidental  agreement  between  phenomena 

1  Novum  Organon,  i.  105.  2  Lotze,  Logic,  p.  343. 


TYPES   OF  INDUCTIVE  INFERENCE  47 

can  be  revealed  only  when  the  underlying  cause  is 
ascertained. 

The  third  method  alone  has  scientific  worth. 
True  induction  must  be  a  continued  search  to  dis- 
cover a  causal  relation. 

3.  The  two  first  processes  fulfil  their  functions 
largely  as  tentative  and  suggestive  methods.  In 
enumeration  of  instances,  we  are  often  led  to  note 
resemblances  which  become  the  basis  of  analogy. 
And  analogy  suggests,  in  turn,  hypothesis  which  is 
capable  of  verification  through  subsequent  experi- 
ment. 

The  question  may  be  put,  "  Which  of  the  three 
processes  is  induction  proper  ?  "  The  fact  is  that 
it  may  involve  all  three,  but  it  is  not  complete  until 
it  reaches  the  third,— the  experimental  method. 
Analogy  is  especially  fertile  in  suggestion.  Scien- 
tific minds  most  carefully  trained  and  versed  in 
scientific  methods  of  research  are  often  most  keen 
in  noting  resemblances,  and  detecting  analogies 
which  become  the  basis  of  their  experiments.  New- 
ton possessed  that  rare  insight  which,  in  spite  of 
the  manifest  dissimilarity  of  the  two  phenomena, 
could  yet  discern  an  essential  likeness  between  the 
fall  of  an  apple  and  the  gravitating  force  of  the 
moon  towards  the  earth. 

4.  It  is  also  to  be  observed  that  the  choice  of 
method  will  depend  largely  upon  mental  habit. 
Some  minds  naturally  or  by  special  training  and 
surroundings  are  given  to  experiment.  They  have 
a  testing  facility  and  inventive  capacity.  Others 
naturally  are  susceptible  in  an  unusual  degree  to 


48  INDUCTIVE  LOGIC 

contrasts  and  resemblances.  Others  again  are  ac- 
customed to  accurate  observation  that  is  ever  push- 
ing beyond  and  seeking  to  extend  its  sphere.  Thus 
we  have  a  natural  division  of  these  methods  accord- 
ing to  psychical  proclivities.  The  choice  of  method 
is  often  conditioned  by  the  force  of  circumstances. 
Experiment  is  not  alway  possible.  Are  all  crows 
black  ?  There  is  no  connection  between  the  general 
organism  of  the  crow  and  its  color  that  has  thus  far 
been  revealed  through  analysis  or  experiment.  The 
only  recourse  is  to  number  instances  over  the  widest 
possible  field.  We  say,  moreover,  that  Mars  may  be 
inhabited ;  for  it  has  an  atmosphere  similar  to  the 
earth  and  therefore  capable  of  sustaining  life. 
Analogy  is  the  only  guide  in  such  a  case,  and  it  is 
impossible  to  verify  it  either  by  observation  or 
experiment. 

5.  All  the  methods  tend  to  one  end,  that  of  ef- 
fecting a  generalization  of  experience.  The  gen- 
eralization may  be  either  a  numerically  general  one, 
or  one  expressed  in  terms  of  a  generic  concept. 

(1)  The  former  consists  in  the  extension  of  several 
instances  to  their  repetition  under  like  conditions. 

(2)  The  second  consists  in  the  extension  of  several 
instances  to  all  cognate  species  under  the  same 
genus. 

Examples  of  these  two  kinds  of  generalization 
are  as  follows  :  The  general  proposition  that  all 
sulphur  is  combustible  is  of  the  former  kind;  all 
instances  are  substantially  of  the  same  nature,  and 
do  not  differ  as  distinguishable  species  under  the 
same  genus,  but  rather  a  repetition  of  like  phenom- 


TYPES   OF   INDUCTIVE  INFERENCE  49 

ena.  The  general  concept  in  the  above  proposition 
is  of  the  nature  of  an  iyifima  species.  On  the  other 
hand,  the  proposition  that  all  mammals  are  verte- 
brates, has  the  subject-term  in  form  of  a  generic 
concept.  Many  species,  differing  widely  among  them- 
selves, may  be  embraced  under  it.^ 

1  Sigwart,  Logic,  Vol.  II.  pp.  310,  311. 


CHAPTER  V 

Causation 

We  have  seen  that  induction  as  a  truly  scientific 
method  consists  in  the  analytical  determination  of 
the  relations  of  cause  to  effect  in  any  complex  phe- 
nomenon, accompanied  by  a  generalization  of  the 
result  obtained.  The  final  outcome  of  such  a  proc- 
ess is  an  universal  concept  which  embodies  a  law, 
expressed  in  terms  of  a  constant  connection  between 
antecedent  and  consequent.  As  Green  has  said, 
"  The  essence  of  induction  consists  in  the  discovery 
of  the  causes  of  phenomena."  ^  A  causal  view  of 
the  universe  gives  rise  to  logical  concepts,  whereas 
a  mythological  view  of  the  universe,  as  in  ancient 
times,  resulted  in  mere  empirical  concepts,  which 
gave  no  assurance  either  of  stability  or  invari- 
ability. It  will  be  necessary,  therefore,  to  de- 
termine more  precisely  the  logical  significance  of 
the  causal  idea,  which  seems  to  underlie  all  induc- 
tive inference.  This  is  no  easy  task.  According  to 
Clifford,  cause  has  sixty-four  meanings  in  Plato,  and 
forty-eight  in  Aristotle.^ 

1  Green,  Phil.  Works,  Vol.  II.  p.  284. 

2  Clifford,  Lectiwes  and  Essays,  Vol.  I.  p.  149. 

50 


CAUSATION  51 

The  causal  idea  has  sometimes  found  expression 
in  the  phrase,  the  uniformity  of  nature,  or  it  is  often 
referred  to  as  the  doctrine  of  universal  causation. 
These  two  phrases  are  often  used  interchangeably ; 
this  gives  rise  to  confusion  of  thought,  for  their 
meanings  are  quite  distinct.  Uniformity  of  nature, 
strictly  interpreted,  means  that  like  antecedents, 
under  precisely  the  same  conditions,  will  be  fol- 
lowed by  like  effects ;  this  idea  expresses  one  phase 
of  causation,  viz.  its  invariability.  The  doctrine  of 
universal  causation,  however,  expresses  the  impos- 
sibility of  phenomena  rising  spontaneously,  without 
an  antecedent,  or  antecedents,  sufficient  rationally 
to  account  for  them.  The  two  ideas  lie  at  the  root 
of  the  causal  idea.     As  Tennyson  has  put  it :  — 

For  nothing  is  that  errs  from  Law. 

Some  confusion  has  also  arisen  from  the  failure  to 
discriminate  precisely  between  the  philosophical  and 
the  purely  logical  questions  relative  to  the  general 
subject  of  causation.  Causation  may  be  viewed 
from  three  different  points  of  view :  — 

1.  What  it  is  phenomenally,  that  is,  as  regards 
its  physical  aspects. 

2.  What  it  is  essentially,  as  regards  its  real 
nature.     This  is  a  metaphysical  question. 

3.  What  it  is  in  respect  to  its  characteristic 
attribute  of  invariability.  This  is  a  purely  logical 
question. 

(1)  As  to  the  first,  what  is  causation  phenome- 
nally? What  is  its  purely  j)hysical  significance? 
Investigations  in  this  line  have  led  to  the  doctrine 


52  INDUCTIVE  LOGIC 

of  the  conservation  of  energy.  This  is  substan- 
tially the  assertion  that,  in  every  event,  no  new 
energy  is  called  forth  which  did  not  exist  before, 
potentially  at  least,  nor  can  any  energy  be  ulti- 
mately lost;  nothing  new  is  created,  —  there  is  only 
a  change  or  transfer  from  one  state  or  condition  to 
another.  Moreover,  the  sum  total  of  energy  in  the 
universe  is  a  constant  quantity;  it  can  neither  be 
added  to,  nor  subtracted  from.  There  is  an  excel- 
lent illustration  of  this  theory  in  the  admirable 
chapter  on  "  Conservation  of  Energy  "  by  Professor 
Tait.  I  give  it  somewhat  in  full :  "  I  allow  an 
electric  current  to  pass  through  a  galvanic  battery 
and  there  is  for  the  moment  a  certain  quantity  of 
zinc  consumed,  or,  as  we  may  put  it,  a  certain  quan- 
tity of  potential  energy  in  the  battery  has  been 
converted  into  the  kinetic  energy  of  a  current  of 
electricity.  That  current  of  electricity  passes  round 
some  yards  of  copper  wire,  coiled  round  a  bar  of 
iron  or  a  number  of  fine  iron  wires  which  are  stand- 
ing vertically  inside  this  apparatus.  The  moment 
the  current  passes,  these  iron  wires  are  converted 
into  magnets,  but,  in  consequence  of  the  conserva- 
tion of  energy,  while  this  is  going  on  they  weaken 
the  current.  The  current  of  electricity  becomes 
weaker  in  the  act  of  making  the  magnet,  but  the 
moment  the  magnet  springs  into  existence,  it  again 
is  weakened,  because,  from  the  necessities  of  its 
position,  its  mere  coming  into  existence  necessitates 
the  passage  of  a  new  current  of  electricity  in  an- 
other coil  of  wire  which  surrounds  this  externally, 
and  finally  this  last  current  we  can  use  to  produce 


CAUSATION  53 

heat,  or  light,  or  sound."  ^  In  this  cycle  of  changes 
we  see  how  closely  connected  even  disparate  phenom- 
ena are,  and  how  the  appearance  of  energy  in  any 
one  definite  state  is  dependent  upon  its  previous 
existence  in  some  other  state.  The  doctrine  of 
conservation  of  energy,  we  shall  see  later  on,  may 
be  suggestive  as  to  the  nature  of  the  analytical 
treatment  of  cause  and  effect. 

(2)  The  philosophical  question  as  to  the  inner 
nature  of  causation  met  with  one  answer  generally 
until  the  time  of  Hume;  namely,  that  the  idea  of 
cause  signified  that  the  antecedent  was  efficient  in 
producing  the  corresponding  consequent,  implying 
the  transfer  of  power  sufficient  to  bring  about  the 
effect.  Hume,  however,  contended  that  in  the 
greatest  possible  extent  of  our  knowledge,  all  that 
we  certainly  know  is  this,  that  one  event  follows 
another.  We  have  no  ground  for  an  assertion 
concerning  the  mamier  in  which  the  sequence  is 
effected,  nor  assume  any  real  tie  between  them. 
Hume  insisted  that  phenomena  were  conjoined,  but 
never  connected.^  His  opponents,  as  Kant  and 
others,  deny  him,  however,  his  fundamental  posi- 
tion, —  that  the  origin  of  the  causal  concept  comes 
from  experience  alone.  They  urged  that  it  has  an 
a  priori  origin,  a  concept  simple  and  unanalyzable, 
given  through  intuitive  insight;  developed  in  the 
sphere  of  experience,  but  not  dependent  upon  expe- 
rience for  its  warrant.  It  is  an  interesting  fact 
that  the  idea  of  the  conservation  of  energy  devel- 

1  Tait,  Recent  Advances  in  Physical  Science,  pp.  76,  77. 

2  Hume,  Essay  on  Idea  of  Necessarij  Causation. 


54  INDUCTIVE  LO(iIC 

oped  subsequent  to  Hume's  time.  It  seems  to  give 
evidence  which  Hume  insisted  was  not  and  could 
not  be  forthcoming,  namely,  concerning  the  idea  of 
the  antecedent  as  an  efficient  power.  Through  the 
modern  doctrine,  the  impression  of  a  transfer  of 
real  power  is  produced,  though  its  mode  and  man- 
ner still  remain  a  mystery. 

(3)  The  logical  aspect  concerns  not  the  phenome- 
nal manifestation  of  cause  and  effect,  nor  their  inner 
nature,  but  rather  the  element  of  invariability  in 
causation.  Two  questions  here  suggest  themselves  : 
First,  Is  invariability  a  fact,  —  a  constant  ele- 
ment in  causation  ?  Second,  How  do  we  account 
for  its  existence  ?  The  first  only  has  truly  logical 
significance.  The  invariability  of  causation,  that 
like  antecedents  under  precisely  the  same  condi- 
tions produce  like  effects,  alone  makes  induction 
possible.  Mill  says  that  it  is  the  belief  in  the 
uniformity  of  nature  which  stands  as  the  ultimate 
major  premise  in  every  process  of  induction. 
Hume  accepted  it,  and  based  inferences  upon  it, 
and  never  challenged  it  as  a  working  basis  as 
regards  the  affairs  of  every-day  life.  He  acknowl- 
edged the  element  of  invariability,  and  only  denied 
the  bond  of  connection.  This  element  has  peculiar 
logical  significance :  without  it,  it  w^ould  be  impos- 
sible to  extend  our  knowledge  beyond  the  seen  and 
the  heard,  indeed  that  which  is  seen  and  heard 
w^ould  then  have  no  meaning,  and  no  basis  for  their 
interpretation  and  appreciation.  Being  assumed, 
however,  in  our  logical  postulate,  we  have  a  basis 
for  induction,  —  a  constant  to  be  sought  for,  and  to 


CAUSATION  55 

be  depended  upon,  in  explanation  of  the  past  and  in 
prediction  of  the  future. 

When  we  come  to  the  second  question,  which  is 
essentially  a  genetic  one,  how  the  belief  in  the  uni- 
formity of  nature  arose,  we  find  two  classes  which 
answer  respectively  that  the  belief  arose  a  priori, 
and  on  the  other  hand,  from  experience  simply. 
The  former  is  the  opinion  especially  associated  with 
the  Scottish  School  of  philosophy.  Hume  holds 
that  it  proceeds  from  a  psychological  law  of  custom 
or  habit,  —  an  unbroken  line  of  mental  associations 
inducing  a  belief  within,  concerning  the  uniformity 
of  nature  without.  Mill  has  also  a  like  empirical 
basis  for  a  belief  in  the  uniformity  of  nature ;  he 
holds  that  having  observed  uniformity  in  many 
experiences,  in  fact  never  contradicted,  we  general- 
ize so  as  to  cover  a  sphere  beyond  our  experience. 
Moreover,  we  possess  the  consensus  of  testimony, 
coextensive  with  the  history  of  humanity,  of  the 
indefinitely  wide  extent  of  the  sphere  of  causation, 
and  the  accompanying  characteristic  of  uniformity. 
His  position  is  fortified  by  the  fact  that  in  the 
process  of  incomplete  induction,  its  probability  is 
strengthened  where  there  has  been  exceptionally 
abundant  scope  for  observation,  so  that  there  is  the 
overwhelming  conviction  that  if  there  had  been  a 
time  or  place  where  the  law  would  prove  untrue,  it 
would  have  been  noticed.  Instead  of  universal 
causation.  Mill  and  his  followers  make  a  more 
cautious  statement ;  causation  as  coextensive 
with  the  sum  total  of  human  experience.  This  is 
abundantly  adequate  to  embrace   all   possible  cir- 


56  INDUCTIVE   LOGIC 

ciimstances  of  practical  inference.  The  immensely 
high  degree  of  probability  engenders  a  subjective 
certitude  Avhich  in  every-day  conduct  of  affairs,  and 
even  in  the  more  exact  requirements  of  scientific 
investigation,  is  never  questioned. 

Preyer  has  given  an  interesting  account  of  the 
extremely  early  appearance  of  the  appreciation  of 
the  causal  relation  in  the  case  of  his  child,  "  who,  at 
the  three  hundred  nineteenth  day  of  its  life,  struck 
several  times  with  a  spoon  upon  a  plate.  It  hap- 
pened accidentally,  while  he  was  doing  this,  that  he 
touched  the  plate  with  the  hand  that  was  free ;  the 
sound  was  dulled,  and  the  child  noticed  the  differ- 
ence. He  now  took  the  spoon  in  the  other  hand, 
struck  with  it  on  the  plate  and  dulled  the  sound 
again,  and  so  on.  In  the  evening  the  experiment 
was  renewed  with  a  like  result.  Evidently  the 
function  of  causality  had  emerged  in  some  strength, 
for  it  prompted  the  experiment.  The  cause  of  the 
dulling  of  the  sound  by  the  hand  —  was  it  in 
the  hand,  or  in  the  plate  ?  The  other  hand  had 
the  same  dulling  effect,  so  the  cause  was  not  lodged 
with  the  one  hand.  Pretty  nearly  in  this  fashion 
the  child  must  have  interpreted  his  sound-impres- 
sion and  this  at  a  time  when  he  did  not  know  a 
single  word  of  his  later  language."  ^ 

The  theoretical  soundness  of  Mill's  speculations, 
however,  has  a  flaw,  although  the  practical  results 
may  not  be  thereby  invalidated.  The  inductive  proc- 
ess, which  is  supposed  to  be  a  truly  scientific  method, 
and  superior  to  induction  by  simple  enumeration 
1  Preyer,  The  Senses  and  the  Will,  pp.  87,  88. 


CAUSATION  57 

must,  according  to  Mill,  at  the  last  analysis,  rest 
upon  a  principle  which  is  itself  based  upon  an  in- 
complete induction.  A  very  fair  and  searching  criti- 
cism of  Mill  is  that  of  Venn's  in  his  Empirical  Logic} 
Whately  insists  that  the  whole  question  concerning 
the  nature  of  our  belief  in  uniformity  is  irrelevant, 
as  it  is  a  purely  psychological  and  not  a  logical 
one.  Mansel  holds  a  mediating  position  in  insist- 
ing that  the  idea  of  universal  causation  is  intuitive, 
while  that  of  uniformity  is  necessarily  empirical. 
Sigwart  has  very  trenchantly  criticised  Mill  in  that 
"taking  away  with  one  hand  what  he  gives  with 
the  other,  he  shows  in  the  uncertainty  of  his 
views  the  helplessness  of  pure  empiricism,  the  im- 
possibility of  erecting  an  edifice  of  universal  j^ropo- 
sitions  on  the  sand-heap  of  shifting  and  isolated 
facts,  or,  more  accurately,  sensations;  the  en- 
deavor to  extract  any  necessity  from  a  mere  sum 
of  facts  must  be  fruitless.  The  only  true  point  in 
the  whole  treatment  is  one  in  which  Mill  as  a  logi- 
cian gets  the  better  of  Mill  as  an  empiricist ;  namely, 
that  every  inductive  inference  contains  a  universal 
principle ;  that  if  it  is  to  be  an  inference  and  not 
merely  an  association  of  only  subjective  validity, 
the  transition  from  the  empirically  universal  judg- 
ment all  known  ^'s  are  B  to  the  unconditionally 
universal  all  that  is  A  is  B,  can  only  be  made  by 
means  of  a  universal  major  premise,  and  that  only 
upon  condition  of  this  being  true  are  we  justified 
in  inferring  from  the  particular  known  ^4's  to  the 
still  unknown  ^'s."  ^ 

1  Venn,  Empirical  Logic,  p.  130.    ^  Sigwart,  Logic,  Vol.  II.  p.  303. 


58  INDUCTIVE  LOGIC 

The  whole  tendency  of  the  modern  logic  is  to 
base  the  causal  postulate  upon  a  ground  which  is 
epistemological ;  namely,  inasmuch  as  our  knowl- 
edge is  one  and  self-consistent  throughout  all  its 
separate  elements,  there  must  be  a  corresponding 
invariability  in  the  phenomena  themselves,  as  there 
is  in  the  system  of  knowledge  which  results  from 
the  interpretation  of  these  phenomena.  This  is 
the  general  view  of  Sigwart,  Bosanquet,  Lotze,  and 
Green.^ 

This  view  may  be  considered  also  as  an  expres- 
sion of  the  Law  of  Sufficient  Keason ;  namely,  that 
there  is  an  inherent  characteristic  of  intelligence 
which  demands  that  every  element  of  conscious- 
ness must  be  referred  to  some  other  element  for  its 
explanation,  and  that  it  is  only  when  the  logical 
connection  of  ideas  corresponds  to  a  real  causal 
connection,  that  the  mind  discovers  a  reason  for 
its  several  experiences  which  is  satisfying.  It  has 
been  said  by  Ueberweg,  as  given  expression  to  this 
view :  "  The  external  invariable  connection  among 
sense  phenomena  is,  with  logical  correctness,  ex- 
plained by  an  inner  conformability  to  law,  accord- 
ing to  the  analogy  of  the  causal  connection  perceived 
in  ourselves  between  volition  and  its  actual  accom- 
plishment." ^ 

There  is  a  distinction  that  is  of  importance  to 
note  between  the  popular  and  the  scientific  idea  of 

1  Sigwart,  Logic,  Vol.  II.  pp.  119, 120;  Bosanquet,  Logic,  Vol. 
II.  pp.  220, 221 ;  Lotze,  Logic,  p.  68 ;  Green,  Phil  Works,  Vol.  II. 
p.  286. 

2  Ueberweg,  Logic,  pp.  281,  282. 


CAUSATION  59 

cause.  The  former  is  the  outcome  of  the  supposi- 
tion that  whatever  immediately  precedes  the  effect 
has  evidently  produced  it,  and  that  this  is  sufficient 
wholly  to  account  for  it.  Such  an  idea  of  causes 
leads,  at  the  best,  but  to  a  loose  and  superficial 
determination  of  the  relation  between  any  ante- 
cedent and  its  consequent,  and  there  is  the  danger, 
moreover,  of  a  hasty  inference  which  results  in  the 
fallacy  of  pos^  hoc  ergo  2)^'opter  hoc.  In  order  to 
attain  a  true  view  of  causation,  we  must  especially 
attend  to  the  extreme  complexity  of  the  causal  con- 
nection. There  is  no  such  thing  as  a  simple  cause 
followed  by  a  simple  effect.  The  cause  is  always  a 
combination  of  several  elements,  circumstances,  and 
conditions;  the  effect  is  always  manifold.  This 
characteristic  has  been  admirably  presented  in 
Mill's  chapter  on  the  '^  Plurality  of  Causes  and  the 
Intermixture  of  Effects.  It  is  well  known  that  the 
variation  in  the  height  of  a  barometer  is  due  partly 
to  the  variation  of  the  atmospheric  pressure,  and 
partly  to  the  variation  of  the  expansion  of  the  mer- 
curial column  due  to  heat.  In  exact  determination, 
some  experiment  or  calculation  must  precede,  before 
there  can  be  a  discrimination  between  the  elements 
of  the  joint  effect.  And  so  also,  a  number  of  cir- 
cumstances may  combine  to  restore  an  invalid  to 
health,  no  one  of  which  alone  being  capable  of 
effecting  his  recovery. 

The  cause  of  any  phenomenon  has  been  defined 
by  Mill,  as  also  by  Brown  and  Herschel,  as  the  sum 
total  of  all  its  antecedents.  This  statement  has 
been  criticised,  inasmuch  as  the  sum  total  of  all 


60  INDUCTIVE  LOGIC 

antecedents  is  indeterminate,  and  that  there  is  no 
end  to  the  possible  ramifications  in  all  directions 
which  an  exhaustive  analysis  of  any  complex  canse 
will  yield.  However,  the  problem  is  one  of  reduc- 
tion to  simplest  possible  terms  within  the  range  of 
our  powers  of  observation  and  experiment.  There 
is  much  in  the  sum  total  of  all  the  antecedents  of 
any  given  effect  which  is  irrelevant.  It  is  the 
peculiar  function  of  logical  analysis  to  discriminate 
between  the  relevant  and  irrelevant.  The  temper- 
ature of  the  laboratory  will  not  affect,  one  way  or 
the  other,  experiments  with  falling  bodies ;  but  will 
essentially  influence  certain  chemical  experiments, 
and  must  enter  as  one  of  the  determining  factors  in 
the  sum  total  of  antecedents.  It  may  be  that  cer- 
tain elements  of  a  complex  whole  may  seem  to  us 
ultimate  and  unanalyzable,  and  yet  be  themselves 
systems  of  more  or  less  complexity.  There  is 
always  a  limit  to  analysis,  both  experimental  and 
mental.  The  analysis  is  to  extend  to  the  ultimate 
parts  as  far  as  possible.  It  is  not  an  exact  process, 
but  a  process  which  tends  to  exactness  to  the  ex- 
tent which  the  scope  of  finite  intelligence  will  per- 
mit. The  reason  is  not  at  fault  so  much  as  the 
natural  limitations  of  observation  and  experimental 
analysis.  The  end  of  our  research  in  causal  analy- 
sis is  to  discover  an  invariable  relation  that  can  be 
expressed  in  the  form  of  an  hypothetical  universal, 
—  If  ^,  then  J5. 

In  order  to  effect  this,  the  complex  A  must  be 
separated  into  its  i)arts,  a,  h,  c,  etc.,  and  the  effec- 
tive, and  necessary,  and  indispensable  element  pro- 


CAUSATION  61 

ducing  B  must  be  determined.  Suppose  it  proves 
to  be  a,  it  may  be  possible  to  subject  this  to  further 
analysis,  and  reduced  to  simpler  elements,  such  as 
X,  y,  z,  etc.,  and  x  found  to  be  the  significant  ele- 
ment of  the  real  cause.  Each  analysis  determines 
a  narrower  and  still  narrower  sphere  within  Avhich 
the  cause  lies.  A  man  is  shot.  We  say  the  bullet 
killed  him ;  then  the  driving  force  behind  the  bul- 
let; then  the  explosive  power  of  the  gunpowder; 
this  in  turn  was  occasioned  by  the  combined  chemi- 
cal and  mechanical  energy  of  its  ingredients,  where- 
by a  solid  is  transformed  into  a  gaseous  substance 
many  times  its  original  bulk. 

Sooner  or  later  we  must  reach  the  end  of  our  an- 
alysis, and  the  investigation  be  necessarily  checked. 
No  explanation  is  ultimate ;  we  only  transfer  our 
point  of  view  from  a  less  to  a  more  familiar  sphere 
of  interpretation.  We  do  not  feel  the  need  of  ex- 
plaining the  very  familiar ;  though  the  most  famil- 
iar is  hardest  satisfactorily  to  explain,  because  there 
is  nothing  simpler  in  whose  terms  we  may  para- 
phrase it.  We  feel  this  in  giving  a  definition  of 
terms  whose  meaning  we  best  know,  and  which  we 
most  frequently  use.  Mr.  Barrett,  a  former  assist- 
ant at  the  Royal  Institution,  said  of  Faraday :  "  I 
well  remember  one  day  when  Mr.  Faraday  was  by 
my  side,  I  happened  to  be  steadying,  by  means  of 
a  magnet,  the  motion  of  a  magnetic  needle  under  a 
glass  shade.  Mr.  Faraday  suddenly  looked  most 
impressively  and  earnestly,  as  he  said :  '  How  won- 
derful and  mysterious  is  that  power  you  have  there  ! 
The  more  I  think  over  it,  the  less  I  seem  to  know.' 


62  INDUCTIVE  LOGIC 

And  yet,  he  who  said  this  knew  more  of  it  than  any- 
living  man."  ^ 

Although  our  knowledge  is  limited  as  in  all  cases 
of  causation,  however  simple,  nevertheless,  as  far 
as  it  goes,  the  several  elements  are  related  logically, 
that  is,  necessarily  and  universally.  We  may  only 
know  in  part,  but  still  we  know,  and  the  world,  as 
interpreted  for  us  in  knowledge,  is  a  world  of 
invariable  sequences.  The  process  of  inductive 
analysis,  therefore,  consists  in  reducing  a  complex 
antecedent  to  its  ultimate  parts,  in  order  to  reveal 
the  element  or  elements  in  it  which  have  caused 
the  given  effect.  It  sometimes  happens  that  differ- 
ent elements  in  an  antecedent  may  be  regarded 
severally  as  the  cause,  according  to  the  psychologi- 
cal point  of  view  as  regards  the  interests  of  the 
investigator.  It  is  not  always  that  a  scientific 
determination  of  the  cause  is  required ;  it  may  be 
that  all  that  is  desired  is  a  knowledge  of  that  part 
of  the  antecedent  which  is  most  closely  and  prom- 
inently connected  with  the  event  in  question.  An 
inquiry  may  be  started  in  reference  to  the  cause  of 
an  epidemic  in  a  community.  One  may  discover 
the  cause  in  the  carelessness  of  sanitary  engineers ; 
another  may  say  the  cause  lies  in  the  poor  construc- 
tion of  the  sewerage ;  another  says  that  the  cause 
of  the  epidemic  is  a  certain  kind  of  bacilli.  Each 
one  is  looking  at  the  chain  of  events  related  as 
cause  and  effect ;  but  they  all  look  at  different  links 
of  the  same  chain.  One  element,  therefore,  of  a 
complex  antecedent  may  be  brought  into  more  or 

1  Gladstone,  Michael  Faraday,  p.  180. 


CAUSATION  63 

less  prominence  as  the  efficient  element  of  the 
cause,  according  as  the  point  of  view  is  shifted. 
If,  in  the  search  for  the  cause  of  phenomena,  the 
sum  total  of  antecedents  were  always  given  exhaus- 
tively, the  explanation  might  become  so  loaded 
down  with  details  as  to  burden  the  mind  and  con- 
fuse, rather  than  clear,  the  understanding. 


CHAPTER   YI 

The  Method    of  Causal  Analysis   and  Deter- 
mination 

It  will  be  well  to  consider  the  various  problems 
which  will  confront  us  in  seeking  to  analyze  a  com- 
plex antecedent  for  the  purpose  of  discovering  its 
cause. 

1.  There  are  problems  where  cause  and  effect 
appear  in  evident  sequence.  There  is  an  antece- 
dent which  is  followed  by  a  consequent.  If  A 
happens,  then  B  will  happen.  Instances  of  this 
kind  most  readily  yield  themselves  to  the  process 
of  analysis,  because  a  change  in  any  given  phe- 
nomenon is  occasioned  by  the  efficiency  of  the  ante- 
cedent which  is  observed  in  connection  with  the 
change  itself.  It  is  easier  to  note  active  than 
passive  relations,  the  dynamic  rather  than  the 
static.  The  attention  is  attracted  and  held  by 
change.  The  bird  flying  across  our  path  is  ob- 
served, and  the  one  perched  upon  the  tree  near 
at  hand,  however  conspicuous  may  be  its  position, 
is  passed  by  without  any  notice  taken  of  it.  It  is 
easier  to  connect  the  moisture  of  the  grass  with 
falling  rain,  than  when  the  same  is  occasioned  by 
the  dew.  In  one  case,  the  causal  relation  is  ex- 
64 


CAUSAL  ANALYSIS   AND  DETERMINATION        65 

liibitecl  in  operation ;  in  the  other,  the  connection 
is  veiled.  We  find  the  grass  wet ;  what  preceded 
it  we  are  not  able  to  see.  There  are  several  in- 
stances of  sequence  among  observed  phenomena 
which  must  be  carefully  discriminated  in  order  to 
avoid  confusion  of  thought.    They  are  as  follows :  — 

(1)  When  we  have  A  followed  by  B,  and  A 
ceases  wholly  while  B  endures  for  an  appreciable 
time  afterwards,  or  it  may  be  permanently.  A 
billiard  ball  strikes  another,  the  second  goes  on 
by  virtue  of  the  newly  acquired  energy  transferred 
by  impact  from  the  first,  Avhich,  however,  stops 
altogether.  I  throw  a  ball  which  lodges  on  the 
top  of  a  building;  the  effect  produced  lasts  per- 
manently, for  the  ball  has  gained  a  gravity  poten- 
tial due  to  the  energy  imparted  to  it  by  the  initial 
throwing.  The  old  formula,  therefore,  does  not 
always  hold  :    "  Cessante  causa  cessat  effectus." 

(2)  Cases  w^here  A  ceases,  and  thereupon  B 
immediately  ceases  also.  If  we  cut  off  the  supply 
of  gas  which  feeds  a  flame,  the  flame  at  once  dis- 
appears. There  are  cases,  however,  when  an  ap- 
preciable time  must  elapse  in  order  that  the 
transferred  energy  in  the  effect  may  be  dissi- 
pated. When  we  shut  our  eyes  the  stimulus  caus- 
ing the  perception  is  cut  off,  and  the  perception 
at  once  is  at  an  end ;  however,  there  are  cases 
where  the  stimulus  being  very  strong,  after-images 
are  induced  which  remain  for  some  time  in  the 
dark  field  after  the  eyes  are  closed. 

(3)  Cases  where  the  antecedent  is  wholly  in- 
adequate to  produce  the  effect,  but  whose  function 


66  INDUCTIVE  LOGIC 

is  merely  to  liberate  potential  energy  already 
stored,  and  waiting  an  occasion  for  its  active 
manifestation.  A  slight  blow  upon  a  piece  of 
dynamite  causes  an  explosion  wliolly  dispropor- 
tionate to  the  striking  force  employed.  As  is 
well  known,  heat  is  often  an  exciting  cause  of 
chemical  action.  In  such  cases  the  real  cause  is 
more  or  less  concealed,  while  that  which  is  appar- 
ent upon  the  surface  is  not  a  cause  so  much  as  an 
occasion  of  the  phenomenon  in  question.  I  touch 
the  pendulum  and  a  clock  starts  and  so  continues  for 
many  hours  ;  the  swinging  pendulum,  however,  is 
only  the  occasion  of  liberating  the  potential  energy  of 
the  wound-up  spring,  and  thence  the  power  which 
runs  the  clock,  pendulum,  Avheels,  hands  and  all. 

2.  We  have  also  instances  not  so  much  of  se- 
quence as  of  concurrence.  The  planets  revolve 
around  the  central  sun ;  here  the  cause  is  constant, 
attended  by  constant  effect.  The  machine  never 
runs  down  ;  nor  has  to  be  wound  up,  so  that  it  can 
be  seen  that  the  cause  antedates  the  effect. 

3.  Oases  of  Coexistence.  —  These  are  more  diffi- 
cult to  analyze,  for  the  phenomena  do  not  here 
appear  as  antecedent  and  consequent  in  the  midst 
of  changing  conditions  and  circumstances.  We 
have  coexistence  of  two  kinds. 

(1)  Coexisting  attributes  in  one  and  the  same 
organism.  They  are  always  found  together.  They 
form  one  generic  concept  and  are  called  by  one 
name.  Cows  have  horns,  cloven  feet,  are  rumi- 
nant, etc.  Dogs  have  their  distinct  and  constant 
characteristics.     The  orange  has  its  correlation  of 


CAUSAL  ANALYSIS  AND  DETERMINATION        67 

color,  taste,  smell.  And  so  we  have  the  so-called 
'^  natural  kinds,"  i.e.  organisms  presenting  an 
unique  and  characteristic  appearance,  differenti- 
ated thereby  from  all  others.  There  are  also 
certain  correlations  of  growth  which  present  a 
constant  relation  between  certain  attributes,  as 
the  fact,  however  we  may  explain  it,  that  cats 
with  blue  eyes  are  invariably  deaf.  There  are, 
moreover,  illustrations  of  the  same  in  an  inorganic 
sphere,  as  the  laAv  which  connects  the  atomic 
weight  of  substances  and  their  specific  heat  by 
an  inverse  proportion;  or  that  other  law  which 
obtains  between  the  specific  gravity  of  substances 
in  the  gaseous  state,  and  their  atomic  weights, 
they  being  either  equal  or  the  one  a  multiple  of 
the  other.  In  many  cases,  the  bare  fact  of  co- 
existence must  be  accepted  without  being  able  to 
explain  the  causal  ground  of  it.  The  several  ele- 
ments present  a  constant  association,  and  that  is 
all  that  can  be  said  about  it.  In  other  cases, 
however,  a  cause  may  be  found  as  regards,  for 
instance,  the  correlation  of  warm-blooded  animals 
always  possessing  lungs.  The  connection  between 
respiration  and  the  generation  of  heat  is  found  to 
depend  upon  chemical  action  as  its  causal  basis. 

(2)  A  relation  of  statics  rather  than  dynamics,  as, 
for  instance,  a  pillar  supporting  a  roof  or  arch,  is 
said  to  be  the  cause  in  the  sense  of  the  sustaining 
cause  of  the  superstructure.  So  also  the  cohesive 
force  which  holds  together  the  particles  of  a  stone. 
In  such  cases  the  energy  inherent  in  the  cause  is  of 
the  nature  of  a  stress  and  strain. 


68  INDUCTIVE  LOGIC 

4.  Under  this  lieacl  are  embraced  the  phenom- 
ena of  vital  growth  or  development.  These  are  the 
most  difficult  of  all  the  causal  problems  to  deter- 
mine ;  for  it  is  required  to  discover  the  inner  neces- 
sity of  essence,  and  how  the  succeeding  stages  of 
development  unfold  through  the  play  of  the  central 
forces  inherent  in  the  very  nature  and  being  of  the 
organism  itself.  Mill  is  content  with  classifying 
organisms  as  different  natural  kinds,  and  he  is  not 
concerned  with  the  reason  why  there  should  be 
such  and  such  kinds,  nor  does  he  attempt  to  discover 
any  law  concerning  these  natural  correlations  and  the 
mode  of  their  growth.  In  inductive  analysis,  our 
concepts  must  not  merely  grasp  what  the  natural 
kinds  are,  but  also  wdiat  has  determined  them  to  be 
w^hat  they  are.  Darwin  puts  special  emphasis  upon 
the  environment  as  affecting  changes  in  organisms 
and  producing  differentiating  modilications  among 
species.  This,  however,  must  be  considered  not  as 
sole  factor,  but  one  w^hich  is  combined  with  inner 
needs  and  necessities.  Moreover,  Darwin  has  drawn 
attention  to  the  fact  that  individual  differences  need 
scientific  explanation  as  well  as  the  common  attri- 
butes, as,  for  instance,  why  some  sheep  are  black, 
and  why  some  pigeons  are  fan-tailed  and  others  are 
not.  In  all  such  considerations  we  must  not  lose 
sight  of  the  fact  that  there  are  two  determining 
factors,  —  the  inner  necessity  of  development ;  and 
the  external  necessity  of  causality,  as  organisms 
are  acted  upon  by  their  environment.^ 

5.  Cases  of  collocation  where  no  one  element  of 

1  Sigwart,  Logic,  Vol.  II.  pp.  322,  330,  331. 


CAUSAL  ANALYSIS   AND  DETERMINATION        69 

the  cause  is  efficient,  but  all  together  they  combine 
to  produce  the  effect.  In  searching  for  the  cause, 
we  must  not  only  find  a  certain  amount  of  energy 
capable  of  producing  the  effect,  but  we  must  also 
discover  what  peculiar  arrangement  of  the  elements 
concerned  must  exist  before  the  energy  in  question 
can  become  operative.  Chalmers  says  that  "  the 
existing  collocations  of  the  material  world  are  as 
important  as  the  laws  which  the  objects  obey,  that 
many  overlook  this  distinction  and  forget  that 
mere  laws  without  collocations  would  have  afforded 
no  security  against  a  turbid  and  disorderly  chaos.  "  ^ 
We  would  naturally  say  that  the  sole  cause  of  water 
boiling  at  212°  is  the  enveloping  heat ;  it  has,  how- 
ever, been  observed  that  on  top  of  Mont  Blanc, 
water  boils  at  180°  instead  of  212°.  This  indicates 
that,  in  addition  to  the  fire,  the  atmospheric  press- 
ure is  an  element  in  the  cause,  very  easily  over- 
looked. Charcoal  and  diamond  are  of  the  same 
substance ;  a  difference  only  in  the  arrangement  of 
the  molecules  results  in  such  radically  different 
combinations.  There  are,  in  the  main,  three  special 
kinds  of  collocations,  as  follows  :  — 

(1)  Cases  of  modifying  circumstance.  A  strong 
wind  blows  down  a  tree ;  this  would  not  have  oc- 
curred had  not  the  tree  been  hollow.  The  hollow- 
ness  of  the  tree  is  here  a  co-operative  circumstance 
that  is  combined  with  the  efficient  cause,  —  the  force 
of  the  wind.  An  instance  where  arrangement  of 
the  elements  concerned  rather  than  their  efficient  en- 
ergies is  productive  of  the  effect,  is  that  of  capil- 

1  Quoted  by  Jevons,  Principles  of  Science,  p.  740. 


70  INDUCTIVE  LOGIC 

larity,  the  rising  of  liquid  in  a  tube  of  exceedingly 
small  bore.  Here  form  is  more  essential  to  the 
effect  than  the  expenditure  of  any  visible  energy. 

(2)  Cases  in  which  certain  negative  conditions 
prevent  the  realization  of  the  effect.  The  plants 
and  shrubs  die  in  a  long  drouth,  because  it  did  not 
rain.  A  train  collides  with  another,  because  the 
red  signal  was  not  exposed  as  it  should  have  been. 
A  match  will  ignite  gunpowder  generally,  but  it 
fails  to  do  so  should  the  powder  prove  to  be  wet. 

(3)  There  are  also  cases  of  counteracting  causes, 
where  the  effect  of  cause  A  is  not  realized,  as  cause 
B  neutralizes  the  force  of  cause  A ;  as  when  an 
anchored  boat  will  not  respond  to  the  pull  of  the 
oar.  Sometimes  the  cause  is  not  wholly  counter- 
acted, or  it  may  be  the  counteracting  cause  more 
than  holds  the  positive  cause  in  check,  and  is  itself 
operative.  The  rise  of  a  balloon  in  the  air  is  due 
to  the  fact  that  the  force  of  gravity  is  more  than 
overbalanced  by  the  expansive  force  of  the  gas 
within  the  balloon;  one  force  pulling  downwards, 
the  other  bearing  up,  and  the  latter  prevailing. 

Mechanical  forces  acting  in  combination  admit 
of  a  resolution  of  their  joint  effect  according  to 
the  theory  of  the  parallelogram  of  forces.  Chemi- 
cal and  vital  forces  cannot  be  treated  in  such  a 
way  at  all.  From  the  character  of  the  elementary 
forces  in  mechanics,  one  can  calculate  their  com- 
bination. In  chemistry,  however,  when  the  ele- 
ments are  given,  the  resulting  compound  cannot 
be  thus  determined.  So,  also,  in  vital  and  mental 
phenomena,  the  necessarily  complex  nature  of  the 


CAUSAL  ANALYSIS  AND  DETERMINATION        71 

elements  involved  prevents  not  only  prediction  of 
resulting  combinations,  but  even  adequate  explana- 
tion of  that  which  may  be  immediately  given  in 
consciousness. 

6.  It  is  necessary,  in  the  investigation  of  causal 
relations,  to  understand  the  different  modes  of  the 
transfer  of  energy,  which  are  as  follows  :  — 

(1)  Molar  or  mechanical,  as  in  the  case  of  a 
billiard-ball  transferring  its  energy  to  another 
through  impact. 

(2)  Molecular,  as  heat,  chemical  and  electrical 
and  magnetic  forces,  light,  etc.  One  passes  into 
another,  as  chemical  force  producing  electric,  elec- 
tric producing  magnetic,  or  producing  •  heat  and 
light. 

(3)  Cases  where  mechanical  force  becomes  mo- 
lecular, as  friction  inducing  heat;  or  cases  where 
molecular  becomes  mechanical,  as  heat  transferred 
into  the  driving  power  of  an  engine,  or  electricity 
applied  as  a  motor.  A  precise  determination  of 
equivalents  can  be  made  between  molar  and  molec- 
ular energy ;  as,  for  example,  it  has  been  found 
that  it  takes  the  same  amount  of  energy  to  raise 
772  pounds  a  distance  of  one  foot  that  it  does  to 
raise  the  temperature  of  one  pound  of  water  1°  F. ; 
or  the  heat  requisite  to  boil  a  gallon  of  freezing 
water  would  lift  1,389,600  pounds  through  a  dis- 
tance of  one  foot. 

As  a  consequence  of  the  doctrine  of  the  transfer 
of  energy,  a  causal  law  can  be  so  stated  as  to  ex- 
press the  fact  that  variations  in  the  antecedents 
will  call  for  corresponding  variations  in  the  effect, 


72  INDUCTIVE  LOGIC 

as,  for  instance,  sncli  a  law  as  the  following :  "  Ee- 
sistance  in  a  wire  of  constant  section  and  material 
is  directly  proportional  to  the  length  and  inversely 
proportional  to  the  area  of  the  cross-section."^ 
The  neglect  of  quantitative  determination  of  the 
proportionate  variations  of  the  antecedent  and  conse- 
quent was  a  glaring  defect  in  the  inductive  systems 
both  of  Mill  and  of  Bacon. 

Through  the  representation  of  the  various  stages 
of  such  variation,  it  is  also  possible  to  establish  the 
upper  and  lower  limits  beyond  which  the  cause  does 
not  produce  the  corresponding  effect ;  as  in  Weber's 
law  concerning  the  relation  of  stimulus  to  sensa- 
tion, that  stimulus  must  increase  geometrically  in 
order  that  the  sensations  increase  arithmetically. 
There  is  an  upper  and  lower  limit  beyond  which 
this  proportion  does  not  hold. 

The  doctrine  of  conservation  of  energy  creates 
the  impression  of  continuous  change  in  causation, 
in  wdiich  the  effect  unfolds  out  of  the  cause.  We 
do  not  think  of  phenomena  under  this  aspect  as 
discrete  events.  More  than  ever,  in  the  light  of 
modern  science,  does  the  old  saying  obtain,  "  Natura 
non  facit  saltum."  We  no  longer  look  for  catas- 
trophic results  in  nature  —  but  regard  causation 
as  a  continuous  transfer  of  potential  energy  into 
kinetic  or  actual  energy. 

We  come  now  to  the  consideration  of  the  method 

by  which  the  causal  analysis  is  mediated.      This 

is   effected   through   observation   and    experiment. 

Observation  is  something  more  than  mere  looking  at 

1  Jeukin,  Electricity  and  Magnetism,  p.  83. 


CAUSAL   ANALYSIS   AND  DETERML\ATION        73 

phenomena;  it  means  concentration  of  attention  for 
the  purpose  of  research;  it  means  discriminating 
insight,  an  appreciation  of  likeness  and  difference ; 
it  means  a  penetration  beneath  surface  appear- 
ances, and  an  apprehension  of  the  essential  features 
of  the  objects  of  perception.  Experiment  consists 
in  modifying  the  elements  which  form  the  complex 
antecedent  in  order  to  observe  the  resultant  effect 
upon  the  corresponding  consequent.  Forces  may 
be  added  or  subtracted;  their  intensity  may  be 
varied,  increased,  or  decreased;  the  circumstances 
■or  conditions  may  be  altered.  Herschel  speaks  of 
observation  and  experiment  as  passive  and  active 
observation.  When  we  interfere  to  change  the 
course  of  nature,  or  to  bring  natural  forces  within 
the  range  of  our  observation,  we  are  experimenting. 
Observation  is  preliminary  to  experiment,  and  sug- 
gests the  lines  along  which  experiment  should  pro- 
ceed. An  observation  that  sees  the  parts  in  the 
whole  and  the  whole  in  the  parts,  is  in  itself  an 
analysis  of  a  phenomenon,  in  course  of  which  proc- 
ess causal  relations  must  be  disclosed.  The  scien- 
tific spirit  demands  absolute  veracity  in  observation. 
One  ought  not  to  be  blind  to  facts  even  though  they 
tend  to  contradict  preconceived  theories.  Bacon 
has  observed  that  "  men  mark  when  they  hit,  never 
mark  when  they  miss."  We  must  strive  against  a 
natural  tendency  to  see  things  as  we  would  have 
them,  and  not  as  they  strictly  are. 

We  must  also  carefully  distinguish  between  ob- 
served facts,  and  inferences  which  we  instinctively 
draw  from  these  facts.     Observation  is  preliminary 


74  INDUCTIVE  LOGIC 

to  an  inductive  inference,  therefore  it  must  not  it- 
self involve  an  inferencCj  or  we  should  be  arguing 
in  a  circle.  An  interesting  illustration  of  the  dif- 
ference between  observation  and  inference  based 
upon  it,  is  narrated  in  the  life  of  Faraday:  "An 
artist  was  once  maintaining  that  in  natural  appear- 
ances and  in  pictures,  up  and  down,  and  high  and 
low,  were  fixed  indubitable  realities ;  but  Faraday 
told  him  that  they  were  merely  conventional  accep- 
tations, based  on  standards  often  arbitrary.  The 
disputant  could  not  be  convinced  that  ideas  which 
he  had  hitherto  never  doubted,  had  such  shifting 
foundations.  *  Well,'  said  Faraday,  'hold  a  walking- 
stick  between  your  chin  and  great  toe ;  look  along 
it  and  say  which  is  the  upper  end.'  The  experiment 
was  tried,  and  the  artist  found  his  idea  of  perspec- 
tive at  complete  variance  with  his  sense  of  reality ; 
either  end  of  the  stick  might  be  called  upper, — 
pictorially  it  Avas  one,  physically  it  was  the  other."  ^ 
This  indicates  how  readily  our  inferences  and 
observations  blend,  and  how  difficult  it  is  to  separate 
them  in  consciousness.  De  Morgan  has  pointed 
out  that  there  are  four  ways  of  one  event  seeming 
to  follow  another,  or  to  be  connected  with  it,  with- 
out really  being  so  :  — 

(1)  Instead  of  A  causing  B,  our  perception  of  A 
may  cause  B.  A  man  dies  on  a  certain  day  which 
he  has  always  regarded  as  his  last  through  his  own 
fears  concerning  it. 

(2)  The  event  A  may  make  our  perception  of 
B  follow,  which  would  otherwise  happen  without 

1  Gladstone,  Michael  Faraday,  pp.  1G5,  1G6. 


CAUSAL  ANALYSIS  AND  DETERMINATION        75 

being  perceived.  It  was  thought  that  more  comets 
appeared  in  hot  than  cold  summers;  no  account, 
however,  was  taken  of  the  fact  that  hot  summers 
would  be  comparatively  cloudless,  and  afford  better 
opportunities  for  the  discovery  of  comets. 

(3)  Our  perception  of  A  may  make  our  percep- 
tion of  B  follow.  This  is  illustrated  by  the  fallacy 
of  the  moon's  influence  in  the  dissipation  of  clouds. 
When  the  sky  is  densely  clouded,  the  moon  would 
not  be  visible  at  all ;  it  would  be  necessary  for  us 
to  see  the  full  moon  in  order  that  our  attention 
should  be  strongly  drawn  to  the  fact,  and  this  would 
happen  most  often  on  those  nights  when  the  sky  is 
cloudless. 

(4)  B  is  really  the  antecedent  event,  but  our 
perception  of  A,  which  is  a  consequence  of  B,  may 
be  necessary  to  bring  about  our  perception  of  B. 
Upward  and  downward  currents  are  continually  cir- 
culating in  the  lowest  stratum  of  the  atmosphere; 
but  there  is  no  evidence  of  this,  until  we  perceive 
cumulous  clouds,  which  are  the  consequence  of  such 
currents.^ 

There  are  certain  natural  limitations  to  obser- 
vation, as  things  too  minute  to  be  seen,  too  swift 
to  be  carefully  examined;  there  are  sounds  which 
some  ears  can  detect,  while  others  cannot,  and 
shades  that  some  eyes  cannot  discriminate.  There 
are  effects  proceeding  from  certain  causes  that  are 
so  slight  that  we  fail  to  observe  them,  and  yet  erro- 
neously infer  that  they  do  not  exist.  Professor 
Tyndall  has  given  a  striking  illustration  of  the  dif- 

1  Quoted  by  Jevons,  Principles  of  Science,  pp.  409-411. 


76  INDUCTIVE  LOGIC 

ference  of  auditory  poAver  in  two  individuals;  he 
says :  "  In  crossing  the  Wengern  Alp  in  company 
with  a  friend,  the  grass  at  each  side  of  the  path 
swarmed  with  insects  which  to  me  rent  the  air  with 
their  shrill  chirruping.  My  friend  heard  nothing 
of  this,  the  insect  music  lying  quite  beyond  his 
limit  of  audition."^  Much  has  been  done  by  in- 
ventive skill  to  increase  our  powers  of  observation, 
and  at  the  same  time  to  render  them  more  accurate, 
as  the  telescope,  microscope,  the  vernier  for  precise 
measurement  of  minute  differences  of  magnitude,  the 
chronograph  for  time  measurements,  self-registering 
thermometers,  the  thermopile,  galvanometers,  etc. 
One  of  the  chief  problems  of  scientific  method  is  to 
overcome  natural  limitations  of  observation  through 
mechanical  devices. 

Observations  on  a  large  scale  and  over  a  consid- 
erable period  of  time  must  sometimes  be  taken  in 
order  to  disclose  tendencies  as  seen  only  in  the 
average  or  the  mean  of  the  observed  results.  Thus 
meteorological,  vital  statistics,  and  others  of  a  like 
kind  must  extend  over  a  large  area,  and  embrace  a 
large  number  of  instances  in  order  to  reach  results 
of  any  value.  It  is  known  that  Tycho  Brahe  made 
an  immense  number  of  most  exact  records  of  the 
positions  of  the  heavenly  bodies  with  the  aid  of  the 
best  of  astronomical  instruments,  and  these  records 
afterwards  became  the  foundation  of  Kepler's  laws 
and  of  modern  astronomy.^ 

The  faculty  for  accurate  observation  can  be  in- 

1  Tyndall,  On  Sound,  pp.  73,  74. 

2  Gore,  The  Art  of  Scientific  Discovery,  p.  310. 


CAUSAL  ANALYSIS   AND  DETERMINATION        77 

creased  by  acquiring  the  habit  of  examining  care- 
fully everything  within  the  field,  of  vision.  We  fail 
to  see  many  things  because  we  fall  into  the  easy  way 
of  passing  them  by  without  noting  their  presence 
or  appreciating  their  significance.  It  was  said  of 
Charles  Darwin  by  his  son  that  "  he  wished  to  learn 
as  much  as  possible  from  every  experiment,  so  that 
he  did  not  confine  himself  to  observing  the  single 
point  to  \vhich  the  experiment  was  directed,  and 
his  power  of  seeing  a  number  of  other  things  was 
wonderful."  ^  The  open-eyed  vision  is  the  prime 
requisite  for  scientific  investigation. 

The  limitations  of  observation  naturally  lead  to 
experiment,  whose  special  function  is  to  so  modify 
phenomena  as  to  bring  a  suspected  causal  element 
more  prominently  into  notice.  This  can  be  done  by 
intensifying  the  force  in  question,  or  by  neutralizing 
all  other  elements  in  combination  with  it,  so  that 
the  sole  effect  of  this  force  in  actual  operation  can 
be  observed.  When  the  cause  is  not  a  simple  ele- 
ment, but  a  combination,  then  the  problem  is  to 
vary  the  conditions  so  that  but  one  possible  com- 
bination, then  another,  can  be  operative  alone,  and 
note  the  corresponding  effect.  Given  a  certain 
number  of  eleinents,  the  number  of  possible  combi- 
nations is  mathematically  determinate,  and  can  be 
tried  seriatim  until  all  possibilities  are  exhausted. 
Venn  has  given  a  long  and  interesting  illustration 
of  this  in  his  Empirical  Logic?  All  combinations 
need  not  be  tried,  however ;  for  many  will  be  seen 

1  Life  and  Letters  of  Charles  Darwin,  VoL  I.  p.  122. 

2  pp.  402  ff. 


78  INDUCTIVE  LOGIC 

to  be  either  impossible  or  irrelevant.  The  aim  is 
to  obtain  an  antecedent  which  shall  consist  either 
of  a  simple  element,  or  a  combination  such  that  with 
its  presence  the  effect  in  question  is  present  also, 
but  with  its  disaj)pearance  the  effect  is  wanting. 

It  is  not  sufficient  to  note  merely  the  presence 
of  an  antecedent  connected  with  a  corresponding 
consequent ;  scientific  determination  consists,  in  ad- 
dition, in  proving  the  absence  of  the  suspected  cause 
in  cases  where  the  given  effect  is  not  present.  This 
is  called  determination  by  negation.  A  proposition 
which  is  held  affirmatively  has  only  a  vague  sig- 
nificance ;  it  must  be  determined  within  definite 
limits  assigned  to  it  by  virtue  of  what  it  is  not. 
Defining  means  to  set  limits  to  a  term  ;  these  limits 
grow  out  of  the  nature  of  the  thing  itself.  The 
negative  judgment  marks  a  transition  always  from 
that  which  is  indefinite  and  incoherent  to  that 
which  is  definite  and  coherent.  For  instance,  we 
have  a  vague  notion  of  chemical  affinity  that  ele- 
ments combine  to  form  compounds.  That  is  the 
nucleus  of  our  knowledge ;  it  grows  in  definiteness 
through  a  continuous  process  of  limitation  by  nega- 
tion. We  find  that  not  all  elements  combine  with 
each  other,  that  they  do  not  combine  except  in  cer- 
tain proportions,  and  that  even  those  which  do  in 
certain  definite  proportions  will  not  combine  in  the 
presence  of  others  having  greater  affinity,  as,  for 
instance,  in  the  presence  of  oxygen,  and  so  on. 
Every  negative  proposition  established  renders  the 
original  one  more  accurate. 

This  may  be  illustrated  also  in  the  concrete,  when 


CAUSAL   ANALYSIS   AND  DETERMINATION        79 

in  dissection  one  is  tracing  a  nerve ;  it  is  followed 
throughout  its  course  by  a  series  of  negative  judg- 
ments though  they  be  unexpressed:  This  is  not  a 
nerve,  but  an  artery ;  this  is  not  a  nerve,  but  a  vein ; 
this  is  not  a  nerve,  but  a  filament,  or  shred  of 
muscle,  etc.  So  we  rise  through  negative  discrim- 
ination to  a  clear  apprehension  of  an  object  under 
investigation.  The  original  proposition  must  be 
readjusted  with  every  new  negative  determination. 
It  sometimes  happens  that  the  original  proposition 
is  completely  negatived  by  the  negative  determin- 
ation, sometimes  again  it  is  confirmed. 

A  proposition  that  has  not  been  worked  over 
through  such  a  process  has  no  real  logical  worth 
or  scientific  value.  Therefore  in  the  analysis  of 
phenomena  when  the  suspected  cause  and  effect 
are  combined  in  a  proposition,  it  can  at  first  be  held 
only  tentatively.  It  must  be  confirmed  negatively, 
or  else  readjusted  to  conform  to  the  negative  re- 
quirements. Suppose  we  have  given  that  A  is 
followed  by  B  as  far  as  we  have  been  able  to  ob- 
serve. We  may  proceed  by  experiment  to  multiply 
instances  of  ^'s  connection  with  B,  but  still  the 
causal  relation  is  not  absolutely  proved.  We  must 
go  on  to  show  that  in  all  cases  of  not-^  there  is  not- 
B,  or  in  all  cases  of  not-B  there  is  not- J..  Negative 
experiment  produces  the  contrapositive,  or  the  con- 
verse contrapositive  of  the  proposition  under  inves- 
tigation, which  deductively  necessitates  the  validity 
of  the  original  proposition. 

This  is  substantially  Mill's  method  of  difference, 
that  if  an  instance  in  which  the  phenomenon  under 


80  INDUCTIVE  LOGIC 

investigation  occurs,  and  an  instance  in  which  it 
does  not  occur,  have  every  circumstance  save  one  in 
common,  and  that  one  occurring  only  in  the  former ; 
the  circumstance  in  which  alone  the  two  instances 
differ,  is  the  effect  or  cause  or  a  necessary  part  of 
the  cause  of  the  phenomenon.  This  method  will 
be  described  later ;  it  is  the  main  inductive  method, 
the  others  being  largely  modifications  of  it.  A 
negative  instance  which  is  established  concerning 
relations  of  not- J.  and  not-B,  is  absolutely  conclu- 
sive, inasmuch  as  not-^  is  the  contradictory  of  A, 
and  not-B  is  the  contradictory  of  B.  They  are 
mutually  exclusive.  No  other  possibility  can  be 
forthcoming,  and  the  experimental  analysis  is  ex- 
haustive. Professor  Tyndall  gives  the  following 
account  of  an  experiment  to  determine  the  cause  of 
resonance.  "  I  hold  a  vibrating  tuning-fork  over  a 
glass  jar  eighteen  inches  deep ;  but  you  fail  to  hear 
the  sound  of  the  fork.  Preserving  the  fork  in  its 
position,  I  pour  water  with  the  least  possible  noise 
into  the  jar.  The  column  of  air  underneath  the 
fork  becomes  shorter  as  the  water  rises.  The  sound 
augments  in  intensity,  and  when  the  water  reaches 
a  certain  level,  it  bursts  forth  with  extraordinary 
power.  I  continue  to  pour  in  water,  the  sound 
sinks,  and  becomes  finally  as  inaudible  as  at  first."  ^ 
From  this  it  is  inferred  that  a  certain  column  of 
water  of  definite  height  is  necessary  to  the  produc- 
tion of  the  sound,  for  above  and  below  the  limits 
no  sound  is  heard.  This  experiment  also  indicates 
that  which  is  most  important  in  causal  determina- 
1  Tyndall,  On  Sound,  p.  172. 


CAUSAL  ANALYSIS   AND  DETERMINATION        81 

tion,  —  a  variation  in  cause  accompaDied  by  a  vari- 
ation in  effect,  as  also  a  maximum  and  minimum 
as  regards  the  intensity  of  the  sound.  Experiment 
proceeds  upon  the  supposition  of  the  nieasurable- 
ness  of  phenomena,  and  seeks  numerically  expres- 
sible results  in  this  regard.  For  instance,  by 
different  experiments,  Tyndall  proved  that  the 
length  of  the  column  of  air  which  resounds  to  the 
fork  in  a  maximum  degree  of  intensity  is  equal  to 
one-fourth  of  the  length  of  the  wave  produced  by 
the  fork.i 

The  negative  determination  of  a  suspected  con- 
nection of  cause  and  effect  must  be  precise  in  order 
to  establish  the  causal  relation  with  that  degree  of 
accuracy  which  is  demanded  in  a  truly  logical  and 
scientific  method.  Upon  this  point,  Bosanquet  has 
a  very  suggestive  passage :  "  The  essence  of  signifi- 
cant negation  consists  in  correcting  and  confirming 
our  judgment  of  the  nature  of  a  positive  phenome- 
non by  showing  that  just  ivhen  its  condition  ceases, 
just  then  something  else  begins.  The  'Just-not'  is 
the  important  point,  and  this  is  only  given  by  a 
positive  negation  within  a  definite  system.  You 
w^ant  to  explain  or  define  the  case  in  which  A  be- 
comes B.  You  want  observation  of  not-jB,  so  that 
you  are  lost  in  chaos.  What  you  must  do  is  to 
find  the  point  within  A  where  A^  which  is  B,  passes 
into  A2  which  is  C,  and  that  will  give  you  the  just- 
not-B  w^hich  is  the  valuable  negative  instance."  ^ 
For  example,  in  Professor  Tyndall's  experiment,  the 

1  Tyndall,  On  Sound,  p.  174. 

2  Bosanquet,  The  Essentials  of  Logic,  p.  134. 

G 


82  INDUCTIVE  LOGIC 

significant  negative  instance  was  this,  —  when  the 
water  in  the  tube  reached  just  that  height  when  for 
the  first  time  during  the  experiment  no  sound  was 
audible.  The  discriminating  observation  that  can 
mark  and  measure  tlie  precise  point  of  transition 
from  sound  to  no  sound,  has  determined  accurately 
the  conditions  necessary  to  produce  the  sound,  and 
precisely  define  their  limitations. 

In  all  observation  and  experiment,  the  following 
possibilities  should  be  kept  before  the  mind  in  order 
to  avoid  a  hasty  conclusion  in  reference  to  a  seeming 
causal  connection.  We  may  think  that  we  have  dis- 
covered the  relation  that  if  there  is  A,  then  there 
must  be  B,  and  the  one  therefore  the  cause  of  the 
other,  but  it  may  happen  that 

1.  Both  A  and  B  are  effects  of  another  cause  and 
are  thereby  related  co-ordinately  in  reference  to  it. 

2.  A  may  be  merely  a  liberating  circumstance, 
or  an  invariable  accompaniment  of  B. 

3.  A  may  not  be  the  cause  of  B,  but  only  an 
element  of  a  complex  collocation  which  is  the 
cause  of  B. 

4.  Each  separate  instance  of  B  may  so  differ  as 
to  respond  to  the  action  of  A  in  a  manner  different 
from  the  others. 

5.  A  may  be  related  to  B  in  a  system  of  such  a 
nature,  that  the  system  iii  continuously  developing 
new  effects  causes  B,  as  the  introduction  of  medicine 
into  an  organism  whose  forces  are  themselves  effect- 
ing a  healing  process. 

6.  It  is  often  very  difficult  to  tell  whether  A  is 
the  cause  of  B,  or  B  the  cause  of  A,  as  in  districts 


CAUSAL  ANALYSIS   AND  DETERMINATION        83 

wliere  drunkenness  and  poverty  are  prevalent,  or 
cases  of  moral  and  intellectual  feebleness.  Which 
is  the  cause  ?  and  which  the  effect  ?  In  many 
cases  such  as  these,  the  forces  react  upon  each 
other,  the  effect  tending  to  increase  the  intensity 
of  the  cause. 

7.  The  connection  of  A  and  B  may  be  one  of 
mere  coincidence,  and  not  of  a  causal  nature  what- 
soever. Newton  was  much  impressed  with  the 
apparent  connection  between  the  seven  intervals  of 
the  octave,  and  the  fact  that  the  colors  of  the  spec- 
trum divide  into  a  like  series  of  seven  intervals. 
And  yet  there  is  no  causal  connection  that  can  be 
proved  to  exist  between  the  two. 

The  more  we  dwell  upon  these  various  possibilities, 
the  more  are  we  impressed  with  the  extreme  com- 
plexity in  Avhich  the  relation  of  cause  and  effect  is 
involved.  The  investigator  must  bring  to  his  re- 
search the  spirit  of  patience  and  perseverance,  as 
well  as  a  clear  vision  and  discriminating  insight. 
Sir  John  Lubbock,  in  his  observations  upon  the 
habits  of  ants,  says  that  at  one  time  he  watched 
an  ant  from  six  in  the  morning  until  a  quarter 
to  ten  at  night,  as  she  worked  without  intermis- 
sion during  all  that  time.^  It  is  to  such  patient 
investigators  that  Nature  reveals  her  secrets. 

1  Sir  John  Lubbock,  Scientific  Lectures,  p.  73. 


CHAPTER  VII 

Mill's   Inductive   Methods  —  The  Method   of 
Agreement 

There  are  various  methods  of  causal  research 
which  have  received  the  name  of  inductive  methods 
and  have  been  especially  associated  with  the  con- 
tribution of  John  Stuart  Mill  to  the  history  of 
logic.  There  are  five  of  these  methods  or  inferen- 
tial processes  as  given  by  Mill,  and  forming  the  in- 
tegral part  of  his  system  of  induction.  They  are 
as  follows :  — 

1.  The  Method  of  Agreement. 

2.  The  Method  of  Difference. 

3.  The  Joint  Method  of  Agreement  and  Dif- 
erence. 

4.  The  Method  of  Concomitant  Variations. 

5.  The  Method  of  Eesidues. 

The  method  of  agreement  consists  in  inferring 
the  existence  of  a  causal  relation,  when  in  a  num- 
ber of  varying  instances  it  is  observed  that  the 
supposed  cause  is  always  accompanied  by  the  phe- 
nomenon in  question,  as  corresponding  effect.  The 
method  of  difference  is  the  comparing  of  an  in- 
stance where  the  supposed  cause  is  present,  accom- 
panied by  the  corresponding  effect,  with  an  instance 
84 


THE  INDUCTIVE  METHODS  85 

having  precisely  the  same  setting,  but  where  the 
supposed  cause  is  withdrawn,  the  effect  also  disap- 
pearing ;  the  inference  of  a  causal  relation  is  then 
permissible.  The  joint  method  of  agreement  and 
difference  is  the  comparing  of  instances  where  the 
supposed  cause  is  present,  with  similar  instances 
where  it  is  absent;  if  the  corresponding  effect  is 
present  in  the  former,  and  absent  in  the  latter  group 
of  instances,  a  causal  relation  may  be  inferred. 
This  differs  from  the  method  of  difference,  that  in 
the  latter  the  same  instance,  now  with,  and  again 
without  the  presence  of  the  suspected  cause,  is  the 
subject  of  observation;  in  the  joint  method  it  is  a 
number  of  instances  with,  compared  with  a  number 
of  similar  instances  without,  the  presence  of  the  sup- 
posed cause.  The  method  of  concomitant  variations 
consists  in  so  modifying  any  given  phenomenon  that 
the  supposed  cause  will  vary  in  intensity ;  then  a 
corresponding  variation  in  the  accompanying  effect 
is  evidence  of  a  causal  relation.  The  method  of 
residues  consists  in  the  analysis  of  a  given  complex 
phenomenon,  in  which  all  elements  save  one  of  the 
antecedent  are  known  to  be  related  in  a  causal 
manner  to  all  elements  save  one  of  the  conse- 
quent ;  then  the  residual  element  of  the  one  may  be 
regarded  as  the  cause  of  the  residual  element  of  the 
other. 

We  will  now  examine  these  methods  more  in 
detail.  The  brief  outline  above  is  intended  merely 
to  give  a  general  idea  of  the  methods,  that  it  may 
lead  to  a  better  understanding  of  the  more  exact 
statement  of  their  nature  and  characteristics. 


86  INDUCTIVE  LOGIC 

The  Method  of  Agreement. — The  more  precise 
statement  of  this  method  is  given  in  the  first  canon 
of  Mill,  Avliich  is  substantially  as  follows  :  — 

If  two  or  more  instances  of  the  phenomenon 
under  investigation  have  only  one  circumstance  in 
common,  the  circumstance  in  which  alone  all  the 
instances  agree  is  the  probable  cause  (or  effect)  of 
the  given  phenomenon,  or  sustains  some  causal 
relation  to  it. 

The  above  is  based  upon  the  causal  axiom  that 
the  constant  elements  which  emerge  in  any  given 
series  of  similar  phenomena  are  to  be  considered  as 
connected  in  some  manner  with  the  cause  of  the 
phenomena ;  but  that  the  variable  elements  are  not 
connected  with  the  phenomena  in  any  causal  man- 
ner whatsoever. 

The  method  of  agreement  is  illustrated  in  the  in- 
vestigation of  the  very  common  phenomenon  of  the 
transformation  of  substances  from  the  solid  to  the 
liquid  state.  What  is  the  one  circumstance  which 
is  always  present  when  we  consider  the  melting  of 
such  widely  different  substances  as  butter,  ice,  lead, 
iron,  etc.  ?  In  all  instances,  to  whatsoever  extent 
they  may  be  multiplied,  of  the  change  from  solid  to 
liquid  states,  heat  has  been  observed  to  be  present, 
and  is  thereby  indicated  as  the  likely  cause  of  the 
phenomenon  in  question.  The  method  may  be 
represented  through  the  use  of  symbols  which,  ac- 
cording to  Mill,  are  the  capital  letters  to  denote 
antecedents,  and  the  smaller  letters  to  denote  cor- 
responding consequents.  Let  the  following  be  a 
number  of  different  instances  with  the  antecedents 


THE  METHOD  OF  AGREEMENT  87 

and  consequents  arranged  in  order,  and  represented 
as  above  indicated :  — 

ABC abc 

ADE o     .     .     .  ade 

AMN amn 

etc.  etc. 

By  inspection  of  sucli  a  table  of  instances  thus 
analyzed,  and  symbolically  represented,  it  will  be 
readily  seen  that  A  is  the  only  element  common  to 
all  the  antecedents,  while  a  is  the  only  one  common 
to  all  the  consequents.  The  inference,  therefore,  is 
that  A  is  the  cause  of  a.  It  has  been  objected  to 
this  system  of  representation  that  it  artificially  ar- 
ranges the  elements  of  antecedent  and  consequent, 
as  though  there  were  a  number  of  distinct  cause- 
elements,  each  connected  with  a  correspondingly 
distinct  eft'ect-element,  and  it  produces  the  impres- 
sion that  it  is  quite  an  easy  matter  to  see  how  these 
causal  pairs  are  thus  separately  related.^  As  nat- 
ure presents  her  phenomena  to  us,  however,  there 
is  such  complexity  throughout,  that  the  analysis 
cannot  readily  distribute  part  to  part  in  appropri- 
ate causal  relations.  To  avoid  such  an  error  in 
notation,  I  have  adopted  the  following  symbols, 
which  will  be  used  hereafter  to  describe  the  various 
methods.  Let  us  take  C  as  the  letter  to  represent 
the  supposed  causal  element,  and  S,  the  entire  set- 
ting of  accompanying  circumstances ;  let  e  denote 
the  corresponding  effect,  and  s  the  sum  total  of  the 
attendant  consequences.  The  causal  relation  will 
1  Venn,  Empirical  Logic,  p.  411. 


88  INDUCTIVE  LOGIC 

be  then  indicated,  according  to  the  method  of  agree- 
ment, as  follows :  — 

S    -\-G s    -\-e 

S'  -^  C s'  -\-e 

S"-hC s"  +  e 

Here  the  setting  changes  throughout,  as  indicated 
by  S,  S',  S",  etc.,  but  C  remains  constant  in  the 
antecedents ;  also  the  corresponding  setting  in  the 
consequents  changes,  as  indicated  by  s,  s',  s",  etc., 
but  e  remains  constant  throughout.  Such  a  nota- 
tion does  not  attemj^t  to  represent  just  which  parts 
of  S  cause  corresponding  parts  of  s,  nor  by  what 
elements  precisely  >S'  differs  from  S'  and  S",  etc. 
It  does  represent,  however,  the  difference  between 
the  variable  and  constant  elements  of  the  table  of 
instances  which  are  arranged  for  comparison,  and 
this  is  the  key  to  disclose  the  causal  relation. 

As  an  example  of  this  method,  let  us  take  the 
physical  law  that  different  bodies  tend  at  the  same 
time  to  absorb  and  to  emit  the  same  waves  of  light. 
It  is  known  that  every  substance  in  burning  gives 
its  own  lines  in  the  spectrum  analysis,  sodium,  for 
instance,  producing  a  very  bright  line  in  the  yellow 
portion  of  the  spectrum  in  a  definite  locality  (Line 
D,  of  Fraunhofer).  If  now,  instead  of  burning 
sodium,  we  interpose  the  vapor  of  sodium  in  the 
path  of  the  ray  which  should  give  a  continuous 
spectrum,  the  phenomenon  is  completely  reversed ; 
at  the  exact  point  where  there  was  a  bright  line  in 
the  spectrum,  a  dark  line  now  appears.  Thus  the 
vapor  of  sodium,  acting  as  a  screen,  absorbs  the 


THE  METHOD  OF  AGREEMENT  89 

rays  which  it  emits  when  it  acts  as  the  luminous 
source.  A  similar  effect  is  observed  in  the  case  of 
vapors  of  iodine,  of  strontium,  of  iron,  etc. ;  and  is 
a  phenomenon,  therefore,  admitting  of  generaliza- 
tion by  induction.^  This  is  according  to  the  method 
of  agreement;  and  we  may  make  the  following 
representation :  — 

Vapor  of  sodium  acting  as  a  screen  =  S     -f  (7 

"       iodine         "         "         "      =  S'    +  C 

"        iron  "         "         "      =S"  +  C 

"        strontium  "         "         "      =  S'"  -{- C 

etc.  etc. 

The  corresponding  consequents  are  :  — 

Eeversing  bright  sodium  line  to  dark  =  S    -f  e 

"  "       iodine        "         "      =  S'   -\- e 

"  "      iron  "         "      =8"  -\- e 

"  "      strontium"         "      =  S"' +  e 

etc.  etc. 

Therefore  we  have  :  — 

/S    +0  .......  s     -{-e 

JS'   -hO s'    -{-e 

jS"  -\-0 s"  -\-e 

S"'-^0 s"'  +  e 

etc.  etc. 

In  this  the  constant  C  of  the  antecedents  is  the 
vapor  of  any  substance  acting  as  a  screen ;  the  con- 
stant e  is  the  reversal  in  each  case  of  the  bright 

1  Saigey,  The  Unity  of  Natural  Phenomena,  pp.  94,  95. 


90  INDUCTIVE  LOGIC 

line  of  the  substance  in  the  spectrum  to  the  corre- 
sponding dark  line  of  the  same.  From  this  it  is 
inferred  that  the  vapor  of  any  substance  acting  as 
a  screen  absorbs  exactly  those  rays  which  it  emits 
when  it  acts  as  the  luminous  source. 

It  is  of  great  importance  that  the  instances  se- 
lected for  observation  or  experiment  be  as  varied  as 
possible,  so  that  widely  differing  phenomena  may 
be  gathered  together.  Then  if  running  through 
them  all  there  is  one  common  element  observed 
among  the  antecedents,  and  one  common  element 
among  the  consequents,  the  greater  the  variation 
among  the  instances  the  more  pronounced  will  be 
the  significance  of  the  constant  elements.  In  the 
illustration  given  the  substances  which  are  so  differ- 
ent as  iron,  strontium,  sodium,  iodine,  etc.,  preclude 
the  possibility  of  the  resultant  phenomenon  de- 
scribed being  due  to  the  peculiar  properties  of  any 
one  metal,  or  group  of  metals.  So  many,  and  so  dif- 
ferent in  kind,  are  taken  as  to  eliminate  the  peculiar- 
ities attached  to  any  one  in  particular.  In  this  re- 
spect, the  method  is  one  of  elimination.  By  varying 
the  instances,  the  non-essential  is  eliminated,  and  the 
essential,  which  remains  as  the  element  common  to 
all,  is  thereby  emphasized,  and  differentiated  from 
all  attendant  circumstances. 

This  method  also  is  one  of  discrimination,  of 
discerning  the  constant  element  under  the  various 
changing  forms  which  it  can  assume,  and  as  such  it 
is  similar  to  the  logical  process  of  the  formation  of 
a  concept.  The  concept  is  the  grasping  of  the 
universal   element  which   is   present   through   the 


THE  METHOD  OF  AGREEMENT  91 

particular  and  concrete  manifestations  of  the  same. 
Through  them  all  there  is  the  like  common  element 
which  is  the  basis  of  the  concept  itself.  So  out 
of  many  particular  instances  the  mind  grasps  the 
elements  which  are  common  to  all,  and  considers 
them  as  related  in  a  constant  and  therefore  causal 
manner  J  which  has  in  itself  the  character  of  a  uni- 
versal concept  and  so  admits  of  being  formulated  in 
the  form  of  a  law  universal,  which  is  the  end  of  all 
induction. 

This  method,  moreover,  is  peculiarly  adapted  to 
observation,  the  collating  of  a  number  of  instances, 
rather  than  to  experiment.  Instances  cannot  al- 
ways be  manufactured,  and  so  it  may  be  beyond 
the  power  of  experiment  to  reproduce  them.  They 
can,  however,  always  be  the  objects  of  research, 
and  as  such  fall  naturally  into  the  field  of  obser- 
vation. 

The  question  may  properly  be  asked  at  this  point. 
How  does  this  method  differ  from  that  of  induction 
by  simple  enumeration  ?  The  latter  we  have  seen 
is  never  satisfactory  because  the  enumeration  can- 
not be  comx^lete,  and  may  be  contradicted  by  an 
enlarged  experience.  This  method,  however,  is 
superior  in  that  it  provides  for  more  than  simple 
enumeration  of  instances  in  which  the  phenomenon 
in  question  has  occurred;  there  must  be  a  corre- 
sponding analysis  of  the  instances,  accompanied  by 
a  discriminating  insight  to  distinguish  the  essential 
from  the  unessential.  Number  of  instances  in- 
creases the  probability  that  the  variable  elements 
have  been  eliminated,  and  enables  the  mind  to  con- 


92  INDUCTIVE  LOGIC 

centrate  upon  the  constant  elements  that  remain 
and  are  thereby  disclosed. 

This  method  primarily  admits  of  application  to 
instances  where  a  sequence  is  observable ;  that  is, 
where  antecedent  can  be  distinguished  from  conse- 
quent by  an  appreciable  time  element.  It  is,  how- 
ever, possible  to  apply  this  method  to  the  investi- 
gation of  coexistences,  where  it  may  show  that  either 
the  coexisting  elements  are  related  as  cause  and 
effect,  or  that  in  some  causal  manner  they  are  the 
correlated  effect  of  some  cause  sufficient  to  account 
for  them  both.  Many  instances  may  be  adduced 
of  the  prevalence  of  poverty  and  crime  associated 
together.  This  may  indicate  a  causal  relation  be- 
tween them,  and  yet  a  sequence  cannot  be  observed 
of  sufficient  definiteness  to  indicate  which  is  the 
cause,  and  which  the  effect.  The  problem  is  thus 
left  indeterminate,  with  the  suggestion  of  some 
other  cause  which  may  possibly  account  for  them 
both.  All  that  the  method  of  agreement  can  at- 
tain, is  by  collecting  a  number  of  instances  of  di- 
verse nature  to  indicate  that  in  some  way  at  least 
poverty  and  crime  are  connected  by  causal  ties. 
The  constant  coexistence  of  attributes  in  one  indi- 
vidual admits  of  a  similar  treatment  and  similar 
results.  The  fact  of  the  high  coloring  of  male  but- 
terflies in  a  large  number  of  instances,  in  reference  to 
a  variety  of  species,  indicates  a  constant  relation  be- 
tween the  fact  of  its  being  a  male  and  the  possession 
of  brilliant  coloring.  This  inseparable  association 
indicates  a  causal  relation,  which,  however,  cannot 
be  more  precisely  determined  by  this  method.     The 


THE  METHOD  OF  AGREEMENT  93 

full  explanation  of  the  phenomenon  requires  some 
supplementary  hypothesis  depending  upon  condi- 
tions not  disclosed  by  this  method,  an  hypothesis 
such  that  the  high  coloring  has  the  special  function 
of  attracting  the  female  butterfly  and  has  been 
intensified  and  developed  by  natural  selection. 

The  method  of  agreement  is  open  to  criticism  at 
several  points,  and  yet  it  must  be  at  the  beginning 
understood  that  this  method  does  not  rank  as  a 
final  method.  We  shall  soon  see  that  it  serves 
rather  as  suggestive  of  and  leading  to  experiments 
according  to  the  method  of  difference,  to  corroborate 
or  disprove  the  results  which  the  method  of  agree- 
ment may  have  attained.  The  chief  criticisms  that 
have  been  made  of  this  method  may  be  summed  up 
as  follows :  — 

1.  The  cause  indicated  by  the  method  of  agree- 
ment is  not  thereby  proved  to  be  the  sole  cause  of 
the  phenomenon  in  question.  We  may  gather  to- 
gether a  number  of  varied  instances  where  an  ex- 
tensive failure  of  crops  in  the  summer  has  caused 
hard  times  during  the  winter  following.  And  yet 
there  may  be,  and  as  a  fact  there  are,  many  other 
causes  which  engender  periods  of  industrial  depres- 
sion. We  may  say,  therefore,  that  this  method  is 
capable  of  establishing,  tentatively  at  least,  an  uni- 
versal proposition  of  the  form.  All  x  is  y,  it  does 
not,  however,  attempt  to  give  any  indication  one  way 
or  the  other,  regarding  the  validity  of  the  converse. 
All  y  is  X.  Knowing  the  limitations  of  a  method, 
does  not  by  any  means  destroy  its  legitimacy  as  a 
method ;  it  rather  increases  its  efficiency  within  its 


94  INDUCTIVE  LOGIC 

proper  spliere,  by  the  more  exact  knowledge  as  to 
the  precise  extent  of  that  sphere  itself. 

2.  It  is  urged  that  while  it  is  possible  to  recog- 
nize in  most,  if  not  in  all  cases,  the  common  element 
in  the  several  effects  of  similar  phenomena,  it  is  not 
so  easy  a  matter  to  differentiate  the  common  ele- 
ment in  the  corresponding  antecedents  by  the  sim- 
ple method  of  agreement  alone.  For  instance,  in 
Bacon's  illustration  of  the  investigation  of  the  cause 
of  heat,  he  cites  such  disparate  phenomena  as  the 
sun's  rays,  friction,  combustion,  etc.  The  element 
of  heat  is  readily  discernible  through  them  all; 
but  wdiat  is  the  common  element  which  operates  as 
cause  in  each  case?  There  is  the  difficulty.  Sig- 
wart  illustrates  this  in  the  case  of  the  phenomenon 
of  death.  The  effect  can  be  easily  detected  as  sim- 
ilar throughout,  but  in  all  the  antecedents  the  only 
property  common  to  them  all  is  life,  and,  therefore, 
w^e  are  led  into  the  fallacy  of  attributing  to  life 
the  cause  of  death. ^  We  must  therefore  acknowl- 
edge that  some  phenomena  may  occur  in  such  a 
variety  and  such  a  number  of  manifestations  as  to 
disguise  the  nature  of  the  cause  under  the  mask 
of  a  generality  too  indefinite  to  be  recognized.  In 
all  such  instances,  the  method  of  agreement  must 
operate  upon  suggestions  received  from  some  other 
source,  as  to  the  nature  of  the  common  element  in 
the  antecedents.  Or,  some  minor  circumstances 
attending  the  effect  may  indicate  more  precisely 
the  nature  of  the  cause,  as,  for  instance,  the  peculiar 
symptoms  associated  w^ith  death  by  drowning. 
1  Sigwart,  Logic,  Vol.  II.  p.  341. 


THE  METHOD  OF  AGREEMENT  95 

3.  The  common  element  in  the  antecedents  may 
prove  to  be  an  unessential  accompaniment  of  all  the 
instances  examined.  Its  presence,  therefore,  may 
have  nothing  whatsoever  to  do  with  the  observed 
effects.  A  number  of  different  medicines,  for  ex- 
ample, may  produce  a  certain  effect  alike  in  all 
instances.  The  only  common  element  that  can  be 
detected  in  the  various  medicines  examined,  may 
be  the  alcohol  which  is  used  as  the  common  vehicle 
of  the  different  drugs,  and  yet  its  effect  may  be 
entirely  inert  as  regards  the  medicinal  qualities  in 
question.  The  common  element  really  efficient  may 
be  overlooked,  and  another  common  element  which 
is  easily  discernible  may  nevertheless  remain  wholly 
inoperative.  This  difficulty  may  be  overcome  by  a 
more  thorough  analysis  of  the  phenomena  observed, 
which  may  be  attained  by  a  judicious  variation  of 
the  instances,  so  as  to  reveal,  in  turn,  the  precise 
effect  of  the  various  simple  elements  which  together 
constitute  the  complex  whole  of  the  phenomenon  in 
question.  The  defects  of  the  method  in  this  respect 
are,  in  a  word,  the  defects  of  induction  by  simple 
enumeration. 

4.  The  cause  may  be  present  in  all  the  antece- 
dents, and,  notwithstanding  the  corresponding  ef- 
fect, not  appear,  and  this,  not  because  the  tw^o  are 
not  related  in  a  causal  manner,  but  because  the 
cause  is  neutralized  by  the  associated  elements 
which  appear  in  combination  with  it  in  the  various 
antecedents.  For  instance,  diphtheria  germs  are  the 
cause  of  diphtheria,  and  have  been  found  accompa- 
nying this  disease  in  all  cases  which  have  been  ob- 


96  INDUCTIVE  LOGIC 

served.  And  yet  their  presence  is  often  noted  when 
the  disease  itself  does  not  develop.  The  tendency 
existing  is  counteracted  by  the  condition  of  the 
organism  at  the  time,  so  that  the  dread  bacilli  are 
inoperative  and  therefore  harmless.  As  we  have 
seen  before,  the  presence  of  the  effect  necessitates 
the  presence  of  the  corresponding  cause ;  but  by  no 
means  is  it  always  true,  that  the  presence  of  the 
cause  necessitates  the  effect.  The  cause  always 
produces  the  tendency  at  least,  which,  however,  may 
be  neutralized. 

5.  This  method  is  often  applied  in  a  very  care- 
less way  to  the  observations  of  persons  who  do  not 
possess  the  power  of  accurate  discrimination,  and 
therefore  observed  coincidences  are  hastily  assumed 
to  be  particular  instances  of  an  universal  law. 
Such  procedure  leads  to  superstition  and  prejudice. 
It  not  only  warps  the  judgment,  owing  to  its  illogi- 
cal nature,  but  it  also  affects  indirectly  the  man's 
moral  view,  as  it  implies  a  weakness  in  character 
as  well  as  in  mind.  This  criticism  refers,  however, 
to  the  abuse  rather  than  the  legitimate  use  of 
this  method  under  such  restrictions  as  have  been 
already  indicated. 

The  chief  function  of  this  method  is  that  of  sug- 
gestion. It  indicates  often  only  the  possibility  of 
the  existence  of  a  causal  relation ;  in  other  cases  it 
leads  to  an  inference  of  high  probability.  In  all 
cases,  however,  it  marks  but  the  preliminary  steps 
of  an  investigation  which  should  be  followed  up  by 
painstaking  experiment.  As  it  is  the  method  of 
observation  chiefly,  it  is  natural  that  it  should  pre- 


THE  METHOD  OF  AGREEMENT  97 

cede  experiment ;  for  it  is  only  by  reflection  upon 
our  observations  that  we  discover  the  nature  and 
relations  of  phenomena,  which  serve  as  data  for 
subsequent  experiment. 

I  have  selected  several  illustrations  to  indicate 
the  various  fields  of  research  in  which  this  method 
of  agreement  has  led  to  satisfactory  results. 

The  first  refers  to  the  relation  between  the 
occurrence  of  financial  crises  and  the  prevalence 
of  over-production.  Guyot,  in  his  Principles  of 
Social  Economy,  gives  the  following  instances : 
An  enormous  consumption  of  capital  in  the  United 
States  in  the  seventies  for  the  construction  of  rail- 
roads, was  followed  by  unusual  commercial  depres- 
sion. Then  the  like  outlay  in  India  for  railway 
construction  by  means  of  loans  and  taxes  which 
absorbed  the  whole  circulating  capital  of  the  Indian 
population,  was  followed  by  a  devastating  famine 
and  general  commercial  paralysis.  Again  in  Ger- 
many there  was  an  enormous  consumption  of  capi- 
tal in  forts  and  armaments  and  general  military 
equipment,  bringing  on  the  crisis  of  1876-1879. 
England  at  the  same  time  was  unduly  supplying 
circulating  capital  to  the  United  States,  Egypt, 
and  her  colonies,  and  a  financial  crisis  was  the 
result.  Through  all  these  varying  instances  and 
others  of  a  like  nature  which  might  be  added,  the 
constant  relation  of  over-consumption  in  the  ante- 
cedents to  the  industrial  depression  evident  in  the 
effect,  indicates  the  one  to  be  the  cause  of  the  other, 
either  in  whole  or  in  part. 

Again,  it  is  narrated   in  Brewster's   Treatise  on 


98  INDUCTIVE  LOGIC 

Optics  tliat  he  accidentally  took  an  impression  from 
a  piece  of  motlier-of-pearl  in  a  cement  of  resin  and 
beeswax,  and,  finding  the  colors  repeated  npon  the 
surface  of  the  wax,  he  proceeded  to  take  other 
impressions  in  balsam,  fusible  metal,  lead,  gum 
arable,  isinglass,  etc.,  and  always  found  the  irides- 
cent colors  the  same.  His  inference  was  that  the 
form  of  the  surface  is  the  real  cause  of  such  color 
effects.^  The  common  element  which  appears  in 
all  the  antecedents  is  evidently  the  same  form 
impressed  upon  each,  which  was  originally  received 
from  the  mother-of-pearl.  The  cause  is,  moreover, 
independent  of  the  nature  of  the  substance  in  each 
case  which  received  the  impression  upon  its  sur- 
face, because  such  a  variety  of  substances  w^as 
chosen  as  to  eliminate  the  individual  nature  of  each 
as  an  influencing  factor  in  the  result.  In  this 
experiment  we  see  the  advantage  of  varying  the 
instances  as  far  as  possible  for  this  very  purpose  of 
eliminating  all  irrelevant  elements.  Similar  experi- 
ments have  proved  like  results  in  reference  to  the 
colors  exhibited  by  thin  plates  and  films.  Here 
the  rings  and  lines  of  color  have  been  found  to  be 
nearly  the  same  whatever  may  be  the  nature  of  the 
substance.  A  slight  variation  in  color  is  due  to 
the  refractive  index  of  the  intervening  substance. 
With  the  exception  of  this,  the  nature  of  the  sub- 
stance is  not  operative  in  producing  the  color  effect, 
but  the  form  alone. 

The   celebrated   scientist,  Pasteur,  in   the  year 
1868  was  carrying  on  his  investigations  as  to  the 

1  Quoted  by  Jevons,  Principles  of  Science,  p.  419. 


THE  METHOD  OF   AGREEMENT  99 

cause  of  the  blight  then  devastating  the  silkworms 
of  France.  One  of  his  experiments  consisted  in 
selecting  thirty  perfectly  healthy  worms  from  moths 
that  were  entirely  free  from  the  corpuscles,  which 
latter  are  the  germs  of  disease,  or  at  that  time  sus- 
pected to  be  the  germs  of  disease.  Then,  rubbing 
a  small  corpusculous  worm  in  water,  he  smeared 
the  mixture  over  the  mulberry  leaves.  Assuring 
himself  that  the  leaves  had  been  eaten,  he  watched 
the  consequences  day  by  day.  One  after  the  other 
the  worms  languished;  all  showed  evidences  of 
being  the  prey  of  the  corpusculous  matter,  and 
finally,  within  one  month's  time,  all  died.  Pas- 
teur's inference  naturally  was  that  the  corpuscles 
had  produced  the  death.  Of  course  his  results 
Avere  not  founded  upon  this  experiment  alone,  but 
other  experiments,  carried  on  in  many  different 
ways,  served  to  corroborate  the  causal  relation 
which  the  experiment  just  described  had  suggested 
as  at  least  highly  probable. 

In  medicine  also  the  method  of  agreement  is 
often  used  with  effect.  Certain  drugs  are  adminis- 
tered in  a  number  of  cases  and  the  results  noted. 
An  uniform  effect  consequent  upon  the  administra- 
tion of  a  given  drug  indicates  a  causal  connection 
capable  of  generalization.  Not  only  are  subjects  in 
disease,  but  also  in  health,  selected,  and  the  effects 
upon  both  the  normal  and  morbid  natures  compared. 
Thus  a  variation  in  instances  is  secured.  If  a  num- 
ber of  different  drugs  produce  like  effects,  the  ques- 
tion at  once  suggests  itself.  What  is  the  property 
common  to  them  all?     The  method  of  agreement 


100  INDUCTIVE  LOGIC 

often  gives  some  indication  of  this,  when  the  elim- 
ination of  the  inert  properties  can  be  accomplished 
through  a  sufficient  variation  of  instances.  The 
difficulty  lies,  however,  in  this  very  thing,  to  so 
vary  the  instances  as  to  disclose  the  efficient  ele- 
ment present  in  them  all.  Various  medicines  pre- 
sent a  complex  nature  of  such  a  character  that  it 
is  extremely  difficult  to  ascribe  the  precise  effects 
which  the  several  component  parts  individually 
exercise. 

The  method  of  agreement  is  also  used,  perhaps 
unconsciously,  in  the  conduct  of  the  every-day 
affairs  of  life.  AMienever  different  phenomena  in 
our  experience  present  certain  characteristics  of  a 
constant  nature,  we  are  at  once  led  to  suspect  a 
causal  connection,  and  to  start  upon  a  more  search- 
ing investigation  of  the  same.  Too  often,  however, 
the  supplementary  investigation  is  omitted,  and  the 
mind  rests  content  with  a  few  surface  resemblances 
that  lead  to  a  hasty  generalization,  without  being 
more  precisely  and  adequately  determined. 


CHAPTER  VIII 
The  Method  of  Difference 

The  method  of  agreement,  as  we  have  seen,  pre- 
sents a  causal  relation  as  a  suggestion,  admitting  of 
a  high  degree  of  probability  it  may  be,  but  requir- 
ing to  be  tested  by  some  more  scientific  method. 
This  is  accomplished  by  the  method  of  difference. 
Here  a  phenomenon  is  observed,  in  which  the 
supposed  cause-element  and  effect-element  appear ; 
then  while  all  other  circumstances  and  conditions 
remain  unaltered,  the  supposed  cause-element  is 
withdrawn,  or  its  force  adequately  eliminated ;  the 
immediate  disappearance  of  the  supposed  effect- 
element  consequent  upon  this,  indicates  a  causal 
relation  existing  between  the  two.  Or  the  experi- 
ment may  be  made  in  a  different  manner,  but  to 
the  same  end ;  that  is,  a  phenomenon  may  be  char- 
acterized by  the  absence  of  both  cause-element  and 
effect-element;  then,  if  the  introduction  of  the 
cause-element  does  not  disturb  the  phenomenon  in 
question,  except  immediately  to  produce  the  effect- 
element,  the  inference  may  be  drawn  that  the  one 
is  the  veritable  cause  of  the  other. 

Canon  of  the  Method  of  Difference.  —  If  an  in- 
stance in  which  the  phenomenon  under  investigation 
101 


102  INDUCTIVE  LOGIC 

occurs,  and  an  instance  in  which  it  does  not  occur, 
have  every  circumstance,  save  one,  in  common,  that 
one  occurring  only  in  the  former,  the  circumstance 
in  which  alone  the  two  instances  differ  is  the  effect, 
or  it  may  be  the  cause,  or  a  necessary  part  of  the 
cause,  of  the  phenomenon. 

This  method  has  manifold  illustration  in  our 
every-day  inferences.  A  person  is  asleep  in  the 
room  with  us,  and  we  hear  the  loud  noise  of  a  slam- 
ming door,  and  observe  the  person  at  once  awakening 
with  a  start  and  exclamation.  AVe  have  no  hesitancy 
in  ascribing  the  awakening  to  the  noise  immediately 
preceding  it.  We  observe  again  some  one  receiving 
a  letter  or  telegram,  and  immediately  upon  opening 
it  the  face  grows  white  with  anxiety  and  fear,  the 
hands  tremble,  and  there  are  shown  general  symp- 
toms of  perturbation.  The  message  received,  we 
say,  has  caused  the  mental  shock  and  physical 
accompaniments. 

Or,  taking  a  simple  experiment  in  quite  another 
sphere,  it  was  observed  by  Boyle,  in  1670,  that  an 
extract  of  litmus  was  immediately  turned  red  by 
the  introduction  of  an  acid.  This  subsequently 
became  a  test  for  the  presence  of  acids,  the  infer- 
ence being  that  an  acid  has  this  capacity  of  chang- 
ing the  litmus  to  a  red  color  from  its  original  blue. 

Professor  Tyndall  describes  an  experiment  to 
prove  that  waves  of  ether  issuing  from  a  strong 
source,  such  as  the  sun  or  electric  light,  are  compe- 
tent to  shake  asunder  the  atoms  of  gaseous  mole- 
cules, such  as  those  of  the  sulphur  and  oxygen 
which  constitute  the  molecule  of  sulphurous  acid. 


THE  METHOD  OF  DIFFERENCE  103 

He  enclosed  the  substance  in  a  vessel,  placing  it  in 
a  dark  room,  and  sending  through  it  a  powerful 
beam  of  light.  At  first  nothing  was  seen;  the 
vessel  containing  the  gas  seemed  as  empty  as  a 
vacuum.  Soon,  along  the  track  of  the  beam,  a 
beautiful  sky-blue  color  was  observed,  due  to  the 
liberated  particles  of  sulphur.  For  a  time  the  blue 
grew  more  intense ;  it  then  became  whitish ;  and 
from  a  whitish-blue  it  passed  to  a  more  or  less  per- 
fect white.  Continuing  the  action,  the  tube  became 
filled  with  a  dense  cloud  of  sulphur  particles  which, 
by  the  application  of  proper  means,  could  be  ren- 
dered visible.^  In  this  series  of  continuous  changes, 
we  find  the  one  antecedent,  giving  initiative  causal 
impulse,  to  be  the  beam  of  light.  It  was  the  one 
element  introduced  which  started  the  several 
changes  leading  to  the  appearance  of  the  sulphur 
visibly  manifested.  The  one,  therefore,  is  to  be 
regarded  as  the  cause  of  the  other. 

It  is  possible  to  represent  this  method  by  means 
of  symbols  in  a  manner  similar  to  that  of  the 
method  of  agreement.  Let  C  be  the  supposed 
cause  and  e  the  effect  corresponding,  while  S  and  s 
denote  the  setting  of  antecedent  and  consequent 
respectively.     We  have,  therefore,  the  following :  — 

S  +  C       s  +  e 

Then,  withdrawing  C,  we  have  the  absence  of  e. 

S       s 

The  inference  then  is  that  C  is  the  cause  of  e. 

^  Tyndall,  Use  and  Limit  of  the  Imagination  in  Science,  p.  33. 


104  INDUCTIVE  LOGIC 

111  the  method  of  agreement,  a  number  of  in- 
stances were  taken  agreeing  only  in  the  posses- 
sion of  two  circumstances,  —  the  cause  and  effect 
elements  common  to  them  all.  In  this  method, 
only  two  instances  are  taken,  and  they  must  be 
precisely  alike,  with  the  one  exception,  —  the  pres- 
ence of  two  circumstances  in  one,  that  is,  the 
cause  and  the  effect  elements,  and  the  absence  of 
the  same  in  the  other.  In  the  method  of  agree- 
ment, we  compare  the  various  phenomena,  to  note 
wherein  they  agree;  in  the  method  of  difference, 
we  compare  the  two  phenomena,  to  note  wherein 
they  differ.  The  logical  axiom  underlying  the  two 
methods  is  substantially  one  and  the  same,  differ- 
ing only  in  its  special  adaptation  in  each  case. 
The  method  rests  on  the  assumption,  which  must 
be  accepted  as  a  fundamental  postulate,  that  what- 
ever can  be  eliminated  from  the  various  instances 
is  not  connected  with  the  phenomenon  under  in- 
vestigation in  any  causal  manner ;  and  the  method 
of  difference  is  based  on  the  postulate  that  what- 
ever cannot  be  eliminated  is  connected  with  the 
phenomenon  by  a  causal  law. 

The  method  of  difference  is  evidently  the  method 
by  negation,  which  has  already  been  indicated  as 
the  truly  scientific  process  in  induction.  It  is  also 
pre-eminently  the  method  of  experiment  rather 
than  observation;  for  the  withdrawal  or  introduc- 
tion of  forces  can  only  be  accomplished  at  will 
when  we  bring  the  phenomena  under  experimental 
control.  At  times.  Nature  herself  may  perform 
the   experiment  for  us,  and  we   stand  simply  as 


THE   METHOD  OF  DIFFERENCE  105 

observers  to  note  the  results.  This  is  especially 
the  case  in  the  catastrophic  phenomena,  such  as 
volcanic  eruption,  earthquakes,  etc.  Generally 
speaking,  however,  the  method  of  difference  is  the 
process  of  man's  manipulation  to  secure  purposed 
results  in  which  a  causal  relation  is  disclosed. 

A  question  naturally  suggests  itself.  What  is  there 
to  determine  the  precise  mode  of  experiment  ?  We 
may  have  given  a  concrete  whole  of  extreme  com- 
plexity. In  our  experiment,  which  element  shall 
we  proceed  to  eliminate,  in  order  to  note  the  re- 
sult? An  answer  may  be  given  us  through  sug- 
gestions received  from  the  results  of  the  method 
of  agreement  which  has  been  already  applied  to 
the  problem.  If  it  is  not  possible  to  avail  one's 
self  of  this  contribution  from  another  sphere  of  in- 
vestigation, then  the  complex  whole  must  be  broken 
up,  as  far  as  possible,  into  its  simplest  component 
parts,  and  one  after  another  these  parts,  singly, 
then  in  pairs,  and  all  other  possible  combinations, 
caused  to  be  withdrawn,  or  their  force  neutralized, 
and  the  results  in  each  case  noted,  as  to  whether  the 
effect  under  investigation  disappears.  The  exhaus- 
tion of  all  possible  combinations  must  yield  some 
definite  result.  Suppose,  for  instance,  there  is  a 
complex  antecedent  involving  four  separable  ele- 
ments, as  A,  B,  C,  D.  Withdraw  severally  A,  B, 
C,  and  D,  noting  results;  then  withdraw,  in  turn, 
AB,  AC,  AD,  BC,  BD,  CD,  that  is,  the  pos- 
sible combinations  of  four  elements  taken  two  at 
a  time  ;  then  withdraw  ABC,  then  BCD,  ABD, 
and  ACD,  that  is,  combinations  of  four  elements 


106  INDUCTIVE  LOGIC 

taken  three  at  a  time.  By  such  a  process  there 
will  be  disclosed  whether  one  element  alone  or 
whether  a  combination  of  two  or  more  have  pro- 
duced the  effect  under  investigation ;  also  whether 
more  than  one  element  or  combination  of  elements 
may  have  caused  the  effect.^  The  practical  diffi- 
culty in  separating  the  elements  of  a  coinplex 
whole,  and  withdrawing  the  several  combinations 
from  the  whole,  renders  this  process  in  many  cases 
impossible.  The  cause,  however,  is  generally  sus- 
pected. It  may  be  suggested  by  the  method  of 
agreeuient,  by  analogy,  or  by  that  insight  which  at 
once  declares  certain  combinations  to  be  impossible 
and  others  irrelevant.  There  is  generally  a  mental 
experiment  in  which  the  judgment  rejects  unlikely 
combinations,  thus  narrowing  the  field  of  investiga- 
tion as  preliminary  to  the  experiments  proper. 

The  method  of  difference  is  open  to  various  criti- 
cisms ;  the  most  important  are  the  following :  — 

1.  In  applying  this  method,  we  may  be  so  easily 
misled,  in  supposing  our  two  instances  are  precisely 
alike,  with  the  one  exception  of  the  presence  or 
absence  of  the  supposed  cause,  and  yet  in  reality 
the  instances  may  differ  radically,  and  yet  we  may 
be  unable  to  detect  this.  A  patient  may  have 
medicine  administered  to  him,  and  begin  at  once 
rapidly  to  recover,  and  yet  the  very  taking  of  the 
medicine  in  itself  may  have  made  such  a  mental 
impression,  inducing  confidence  and  hope,  that  the 
real  cause  of  the  recovery  may  be  due  wholly  to 

1  This  process  lias  been  illustrated  and  criticised  at  length  in 
a  striking  manner  by  Venn,  Empirical  Logic,  pp.  401  ft. 


THE   METHOD   OF   DIFFERENCE  107 

this  mental  reaction.  Persons  taking  pills  com- 
posed of  inert  snbstances  have  often  given  evidence 
of  bodily  effects  wholly  impossible  to  trace  to  the 
medicine  itself.  And  yet  this  criticism  is  one  of 
caution  rather  than  of  censure  ;  for  the  defects  are 
but  difficulties  which  extreme  care  and  insight  may 
overcome. 

2.  It  has  been  objected  that  this  method  may 
point  out  the  cause  in  the  concrete  instance  before 
the  experimenter,  but  that  this  furnishes  no  basis 
whatsoever  for  a  wider  generalization  that  the  effect 
in  question  is  always  produced  by  this  cause.  Sig- 
wart  has  illustrated  this  objection  by  the  instances 
in  which  typhus  fever  has  been  traced  to  the  drink- 
ing of  impure  water. ^  The  causal  relation  may  be 
fully  established  in  the  cases  investigated,  but  the 
universal  proposition  does  not  follow  that  wherever 
typhus  fever  appears,  impure  water  has  been  drunk. 
This  objection  applies  especially  to  cases  of  extreme 
complexity,  where  proximate  causes  alone  can  be 
discovered,  and  their  ultimate  nature,  which  may 
appear  in  various  forms,  is  not  revealed;  for  in- 
stance, the  impure  water  is  not  in  itself  the  ultimate 
cause  of  the  typhus  fever.  It  contains  the  poison 
germs,  the  real  cause ;  they  may  be  introduced  into 
the  system  in  some  other  way.  .  Care,  therefore, 
should  be  taken  to  reveal  the  cause  in  and  by  itself, 
and  not  the  cause  of  the  cause.  The  objection, 
therefore,  may  be  in  a  measure  overcome.  To 
effect  a  generalization,  moreover,  of  logical  valid- 
ity, it  is  necessary  to  supplement  the  method  of 

1  Sigwart,  Logic,  Vol.  H.  p.  420. 


108  INDUCTIVE  LOGIC 

difference  by  hypothesis   and   subsequent  verifica- 
tions, which  will  be  described  later  on. 

3.  This  method  may  lead  to  error  in  cases  where 
the  supposed  causal  element  is  regarded  as  the 
cause  in  its  entirety,  when  it  is  in  reality  but  a  part 
of  the  cause.  If  one  should  plant  seed  in  a  garden 
and  water  only  one  half  of  the  plot,  and  it  should 
follow  that  only  the  watered  part  brought  forth  the 
leaf  and  flower,  then  an  inference  according  to 
the  method  of  difference  might  be  drawn  that  the 
water  caused  the  sprouting  of  the  young  plants. 
And  yet  it  must  be  regarded  simply  as  contributory 
to  the  real  cause.  Such  a  difficulty  may  be  obvi- 
ated by  a  careful  discrimination  in  the  analysis  of 
the  phenomenon  investigated. 

4.  Sometimes  a  liberating  cause  may  be  revealed 
by  a  strict  interpretation  of  the  method  of  differ- 
ence, when  the  real  cause  is  more  obscure,  and  may 
be  overlooked.  A  stone  may  strike  a  can  of  dyna- 
mite and  the  explosion  which  occurs  may  be  traced 
to  the  impact  of  the  stone.  It  is  the  one  element 
of  difference  introduced  in  the  sphere  of  the  ob- 
served phenomena,  with  the  consequent  result. 
The  force  existing  as  a  potential  is  naturally  ob- 
scure, and  apt  to  elude  observation.  Therefore, 
whenever  a  cause  disclosed  by  the  method  of  dif- 
ference seems  to  be  out  of  all  proportion  to  the 
effect,  it  at  once  suggests  the  probability  that  a 
potential  force  not  discerned  by  our  powers  of  ob- 
servation has  been  the  real  cause,  and  the  former 
a  conditioning  cause  merely.  Another  illustration 
of  this  is  the  experiment  of  Priestley  which  led  to 


THE  METHOD  OF  DIFFERENCE  109 

his  discovery  of  oxygen  in  1774.  He  placed  some 
oxide  of  mercury  upon  the  top  of  quicksilver  in 
an  inverted  glass  tube  filled  with  that  metal  and 
standing  in  mercury ;  he  then  heated  the  oxide  by 
means  of  a  glass  lens  and  the  sun's  rays,  and  ob- 
tained a  gas,  which  he  called  ''  nitrous  air,"  after- 
wards designated  as  oxygen.  The  heat  in  this  case 
was  the  sole  element  of  difference  between  the  two 
instances,  one  in  which  there  was  no  gas,  and  the 
second  after  application  of  the  heat,  when  the  gas 
was  present.  Here  the  heat  must  be  regarded  as 
the  liberating  and  not  in  any  sense  the  producing 
cause.  Again,  as  Lotze  says,  "the  fact  that  with 
the  destruction  of  a  single  part  of  the  brain  a  defi- 
nite psychical  function  ceases,  is  no  proof  that  just 
this  single  part  was  the  organ  which  alone  pro- 
duced that  function."  ^ 

In  addition  to  the  difficulties  attending  this 
method  which  have  been  enumerated  and  which 
have  to  do  with  the  logical  theory  of  the  method, 
there  are  also  difficulties  of  a  practical  nature  which 
arise  in  the  actual  application  of  this  method  in  ex- 
perimental inquiry.     They  are  as  follows  :  — 

1.  Care  must  be  taken  that,  in  the  two  phe- 
nomena compared,  with  and  without  the  supposed 
cause,  there  shall  not  be  an  interval  of  time  elaps- 
ing, in  which  period  some  other  cause  might  be 
introduced  unknown  to  the  investigator,  and  yet 
capable  of  producing  the  result,  or  else  of  neutraliz- 
ing some  force  that  is  present  and  itself  capable  of 
producing  the  result.     For  instance,  if  a  chemical 

1  Lotze,  Logic,  p.  322. 


110  INDUCTIVE  LOGIC 

compound  be  left  for  an  appreciable  time,  we  may 
notice  certain  changes  and  be  able  to  assert  posi- 
tively that  no  new  element  has  been  introduced, 
and  yet  the  action  of  the  air  may  in  itself  have 
been  sufficient  to  work  these  changes.  When  the 
two  phenomena  to  be  compared  can  be  presented 
for  inspection  simultaneously,  this  difficulty  is  obvi- 
ated. This  is  illustrated  in  an  experiment  devised 
to  exhibit  the  presence  of  light  effects  in  the 
spectrum  beyond  the  violet  rays;  that  is,  beyond 
the  place  where  the  spectrum  seems  to  end.  A 
sheet  of  paper  is  taken,  the  lower  part  of  which  is 
moistened  with  a  solution  of  sulphate  of  quinine, 
while  the  upper  part  remains  dry.  Let  the  image 
of  the  solar  ray  fall  upon  this  sheet ;  the  spectrum 
preserves  at  the  top  of  the  sheet  in  the  dry  portion 
of  the  paper  its  ordinary  appearance,  while  in  the 
moistened  portion  a  brilliant  phosphorescence  ai> 
pears  beyond  the  region  of  the  violet  rays.  Here 
the  dry  and  wet  portions  are  simultaneously  pre- 
sented, and  there  is  but  one  point  of  difference  be- 
tween the  two.  The  inference,  therefore,  is  readily 
drawn  that  the  solution  of  sulphate  of  quinine  is  a 
substance  sensitive  to  the  ultra-violet  portion  of  the 
sun's  rays,  the  phosphorescence  being  the  effect  of 
these  rays  upon  the  solution. 

2.  Extreme  care  must  be  taken  that,  in  the  with- 
drawing of  any  element  in  the  course  of  the  experi- 
ment, no  other  element  is  inadvertently  introduced, 
and  that,  in  adding  any  element,  no  existing  element 
or  combination  of  elements  is  destroyed,  or  their 
effect  neutralized.     Mr.  Venn  has  admirably  illus- 


THE   METHOD  OF  DIFFERENCE  111 

trated  this  difficulty,  and  I  give  the  following 
quotation  in  full  from  him :  ^'  We  suppose  that 
when  we  have  put  a  weight  into  one  pan  of  a  pair 
of  scales  we  have  done  nothing  more  than  this,  or 
can  at  any  rate  by  due  caution  succeed  in  doing 
nothing  more.  But  if  we  exact  the  utmost  rigidity 
of  conditions,  we  easily  see  that  we  have  done  a 
great  deal  more.  Our  bodies  are  heavy,  and  there- 
fore the  mere  approach  to  the  machine  has  altered 
the  magnitude  and  direction  of  the  resultant  attrac- 
tion upon  the  scales.  Our  bodies  are  presumably 
warmer  than  the  surrounding  air;  accordingly,  we 
warm  and  therefore  lighten  the  air  in  which  the 
scales  hang,  and  if  the  two  scales  and  their  con- 
tents are  not  of  the  same  volume,  we  at  once  alter 
their  weight  as  measured  in  the  air.  Our  breath 
produces  disturbing  currents  of  air.  Our  approach 
affects  the  surface  of  the  non-rigid  floor  or  ground 
on  which  the  scales  stand,  and  produces  another 
source  of  disturbance,  and  so  on  through  the  whole 
range  of  the  physical  forces."  ^ 

In  the  Report  of  the  British  Association,  1881,  an 
account  is  given  of  Professor  G.  H.  Darwin's  exper- 
iments to  measure  the  lunar  disturbance  of  gravity 
at  the  Cavendish  Laboratory  by  means  of  an  ex- 
tremely delicate  pendulum.  It  was  found  that 
approaching  the  pendulum  in  order  to  observe  its 
reading,  the  surface  level  of  the  stone  floor  on 
which  the  instrument  stood  was  deflected  by  the 
weight  of  the  observer.  As  he  stood  to  take  the 
reading,  the  shifting  of  his  weight  from  one  leg  to 

1  Venn,  Empirical  Logic,  p.  416. 


112  INDUCTIVE  LOGIC 

the  other  was  perceptible ;  so  it  became  necessary 
to  observe  the  reading  by  a  telescope  from  a  dis- 
tance, or  to  adopt  some  similar  plan.^ 

Faraday  was  able  at  will  to  produce  or  remove 
a  magnetic  force,  through  the  revealed  properties 
of  the  electromagnet.  Many  of  his  experiments 
would  have  been  impossible  if  it  had  been  neces- 
sary to  remove  a  cumbersome  magnet  and  reinstate 
it  again  and  again  in  his  experiments.  The  electro- 
magnet, however,  could  produce  or  destroy  the 
presence  of  magnetic  force  without  any  incidental 
perturbations.  Thus  Faraday  was  enabled  to  prove 
the  rotation  of  circularly  polarized  light  by  the 
fact  that  certain  light  ceased  to  be  visible  when 
the  electric  current  of  the  magnet  was  cut  off, 
and  instantly  reappeared  when  the  current  was 
re-established.  Faraday  says  of  the  experiment 
himself:  "These  phenomena  could  be  reversed  at 
pleasure,  and  at  any  instant  of  time,  and  upon  any 
occasion,  showing  a  perfect  dependence  of  cause 
and  effect."  ^ 

3.  In  some  cases  it  is  impossible  to  remove  an 
element  which  is  supposed  to  be  the  cause  of  an 
effect  under  investigation.  Its  removal  might  cause 
the  destruction  or  the  impairing  of  the  whole  phe- 
nomenon. The  force,  therefore,  that  cannot  be 
eliminated  must  be  neutralized  by  an  equal  and 
opposing  force.  For  instance,  the  force  of  gravity 
cannot  be  eliminated;  it  must,  therefore,  be  coun- 
terbalanced by   some    device    of   the  investigator. 

1  Quoted  by  Venn  in  Empirical  Logic,  p.  419. 

"^  Experimental  Researches  in  Electricity,  Vol.  III.  p.  4. 


THE   METHOD   OF   DIFFERENCE  113 

In  chemistry  the  removal  of  an  element  from  a 
compound  may  be  impossible  without  destroying 
utterly  the  compound  itself;  in  such  a  case,  also, 
a  neutralizing  agent  must  be  introduced.  Darwin 
wished  to  prove  that  the  odor  of  flowers  is  attrac- 
tive to  insects  irrespective  of  the  attraction  of 
color.  He  therefore  covered  certain  flowers  with 
a  muslin  net,  which  still  attracted  the  insects  to 
them.^ 

The  following  illustrations  may  serve  further 
to  exhibit  the  various  features  of  the  method  of 
difference :  — 

Mr.  Robert  Mallet  gives  the  following  interesting 
account  of  his  visit  to  Faraday  :  "  It  must  be  now 
eighteen  years  ago  when  I  paid  him  a  visit,  and 
brought  some  slips  of  flexible  and  tough  Muntz's 
yellow  metal,  to  show  him  the  instantaneous 
change  to  complete  brittleness  with  rigidity  pro- 
duced by  dipping  into  pernitrate  of  mercury  so- 
lution. He  got  the  solution  and  I  showed  him 
the  facts ;  he  obviously  did  not  doubt  what  he 
saw  me  do  before  and  close  to  him  ;  but  a  sort 
of  experimental  instinct  seemed  to  require  he 
should  try  it  himself.  So  he  took  one  of  the 
slips,  bent  it  forward  and  backward,  dipped  it, 
and  broke  it  up  into  short  bits  between  his  own 
fingers.  He  had  not  before  spoken.  Then  he 
said,  'Yes,  it  is  pliable,  and  it  does  become  in- 
stantly brittle.'  "  ^  Here  the  experiment  with  and 
without  the  significant  antecedent  and  consequent 

1  Darwin,  Cross  and  Self  Fertilization,  p.  374. 

2  Gladstone,  Michael  Faraday ,  p.  175. 

I 


114  INDUCTIVE  LOGIC 

result  indicates  the  causal  relation,  especially  as 
the  instantaneous  effect  precludes  the  possibility 
of  the  operation  of  any  other  cause. 

Another  experiment  of  Faraday's  is  that  of  his 
investigation  of  the  behavior  of  Lycopodium  pow- 
der on  a  vibrating  plate.  It  had  been  observed 
that  the  minute  particles  of  the  powder  collected 
together  at  the  points  of  greatest  motion,  whereas 
sand  and  all  heavy  particles  collected  at  the  nodes, 
where  the  motion  was  least.  It  occurred  to  Fara- 
day to  try  the  experiment  in  the  exhausted  re- 
ceiver of  an  air  pump,  and  it  was  then  found  that 
the  light  powder  behaved  exactly  like  heavy  pow- 
der. The  inference  was  that  the  presence  of  air 
was  the  coudition  of  importance,  because  it  was 
thrown  into  eddies  by  the  motion  of  the  plate, 
and  carried  the  Lycopodium  powder  to  the  points 
of  greatest  agitation.  Sand  was  too  heavy  to  be 
carried  by  the  air.^ 

Sir  John  Lubbock  gives  an  account  of  experi- 
ments performed  upon  insects  to  prove  that  the 
sense  of  smell  is  in  some  way  connected  Avith 
their  antennae.  One  experiment  was  performed 
by  Forel,  who  removed  the  wings  from  some  blue- 
bottle flies  and  placed  them  near  a  decaying  mole. 
They  immediately  walked  to  it,  and  began  licking 
it  and  laying  eggs.  He  then  took  them  away,  and 
removed  the  antennae,  all  other  circumstances  re- 
maining the  same  as  before,  after  which,  even 
when  placed  close  to  the  mole,  they  did  not  ap- 
pear to  perceive  it.     Another  experiment  similar 

1  Jevons,  Frinciples  of  Science,  p.  419. 


THE  METHOD  OF  DIFFERENCE  115 

to  this  was  tried  by  Plateau,  who  put  some  food 
of  which  cockroaches  are  fond  on  a  table  and 
surrounded  it  with  a  low  circular  wall  of  card- 
board. He  then  put  some  cockroaches  on  the 
table  ;  they  evidently  scented  the  food,  and  made 
straight  for  it.  He  then  removed  their  antennae, 
after  which,  as  long  as  they  could  not  see  the 
food,  they  failed  to  find  it,  even  though  they 
wandered  about  quite  close  to  it.^ 

Another  experiment  is  that  of  Graber  to  prove 
the  sense  of  hearing  in  insects.  He  placed  some 
water-boatmen  {Corixa)  in  a  deep  jar  full  of  water, 
at  the  bottom  of  which  was  a  layer  of  mud.  He 
dropped  a  stone  on  the  mud,  but  the  beetles,  which 
were  reposing  quietly  on  some  weeds,  took  no 
notice.  He  then  put  a  piece  of  glass  on  the  mud, 
and  dropped  a  stone  on  to  it,  thus  making  a  noise, 
though  the  disturbance  of  the  water  was  the  same 
as  when  the  stone  was  dropped  on  the  mud.  The 
water-boatmen,  however,  then  at  once  took  flight.^ 

An  illustration  of  the  method  of  difference  occurs 
in  the  so-called  hlhid  experiments,  which  are  often 
made  in  chemistry  especially.  As  Professor  Jevons 
has  described  such  an  experiment :  "  Suppose,  for 
instance,  a  chemist  places  a  certain  suspected  sub- 
stance in  Marsh's  test  apparatus  and  finds  that  it 
gives  a  small  deposit  of  metallic  arsenic,  he  cannot 
be  sure  that  the  arsenic  really  proceeds  from  the 
suspected  substance;  the  impurity  of  the  zinc  or 

1  Lubbock,  On  the  Senses,  Instincts,  and  Intelligence  of  Ani- 
mals, p.  45. 

2  Lubbock,  On  Senses,  etc.,  p.  75. 


116  INDUCTIVE  LOGIC 

sulphuric  acid  may  have  been  the  cause  of  its  ap- 
pearance. It  is  therefore  the  practice  of  chemists 
to  make  what  they  call  blind  experiments,  that  is, 
to  try  whether  arsenic  appears  in  the  absence  of  the 
suspected  substance.  The  same  precaution  ought 
to  be  taken  in  all  important  analytical  operations. 
Indeed  it  is  not  merely  a  precaution,  it  is  an  essen- 
tial part  of  any  experiment.  If  the  blind  trial  be 
not  made,  the  chemist  merely  assumes  that  he 
knows  what  would  happen."  ^ 

1  Jevons,  Principles  of  Science,  p.  433. 


CHAPTER   IX 

The  Joint  Method  of  Agreement  and  Dif- 
ference 

It  has  already  been  shown  that  the  method  of 
difference  is  sometimes  not  available,  inasmuch  as 
it  may  be  neither  possible  nor  practicable  to  remove 
from  the  phenomenon  to  be  investigated  the  sus- 
pected causal  element  without  destroying  the  phe- 
nomenon itself.  Sometimes,  too,  it  is  impossible 
even  to  neutralize  the  effect  of  the  causal  element 
if  it  is  allowed  to  remain  as  an  integral  part  of  the 
phenomenon.  This  is  especially  the  case  in  all 
vital  phenomena,  and  also  in  many  chemical  phe- 
nomena. Therefore  another  method  is  resorted  to, 
which  is  known  as  the  joint  method  of  agreement 
and  difference.  Inasmuch  as  the  suspected  causal 
element  cannot  be  removed,  we  must  select  another 
phenomenon  as  much  like  the  former  as  possible, 
which  is,  however,  characterized  by  the  absence  of 
the  causal  element.  By  the  simple  method  of  dif- 
ference, two  instances  only  need  be  compared,  the 
one  with  and  the  other  without  the  causal  element, 
but  agreeing  precisely  in  every  other  particular. 
In  the  joint  method,  the  instances  with  and  without 
117 


118  INDUCTIVE  LOGIC 

the  causal  element,  differ  it  may  be  in  several  par- 
ticulars. A  number  of  varying  instances  must 
therefore  be  selected  so  as  to  eliminate  the  possi- 
bility of  any  of  these  differing  charaxjteristics  being 
the  cause  in  question.  Therefore  two  sets  of  in- 
stances are  collected,  and  compared.  The  one  set 
comprises  all  the  positive  instances  having  the  pres- 
ence of  the  supposed  causal  element,  and  the  second 
set  consists  of  the  negative  instances  having  the 
supposed  causal  element  absent  altogether.  The 
validity  of  the  method  depends  upon  the  similarity 
of  the  two  sets  of  instances.  As  the  similarity 
increases,  the  method  approximates  to  the  simple 
method  of  difference. 

The  Canon  of  the  Joint  Method.  —  If  several 
instances  in  which  the  phenomenon  occurs  have 
only  one  circumstance  in  common,  while  several 
instances  in  which  it  does  not  occur  have  nothing 
in  common  save  the  absence  of  that  circum- 
stance; the  circumstance  in  which  alone  the  two 
sets  of  instances  differ,  is  the  effect,  or  cause,  or  a 
necessary  part  of  the  cause,  of  the  phenomenon. 

The  symbolical  representation  of  this  method 
may  be  exhibited  as  follows,  using  a  similar  nota- 
tion to  that  employed  in  the  previous  methods :  — 

I.   Table  of  positive  instances. 

S     -^C s     +e 

>S"    -f-C s'    +e 

;S"  4-0 s"  +e 

>S'"+0  .......  s"'-|-e 

etc.  etc. 


METHOD  OF  AGREEMENT  AND  DIFFERENCE     119 
II.   Table  of  negative  instances. 

^.  ^. 

^n  'n 

^in ^u, 

etc.  etc. 

In  the  two  sets  of  instances,  the  following  con- 
ditions must  be  observed  in  order  to  render  the 
method  valid :  — 

1.  S+C,  S'-\-  C,  S"  -f  C,  S'"  +  C,  etc., 

must  be  so  varied  that  they  reveal  but  one  constant 
element,  common  to  them  all,  as  C.  It  may  be  that 
S  will  resemble  S'  in  more  marks  than  the  one, 
namely  C,  and  this  may  be  true  of  any  two  or  more 
instances ;  however,  taken  all  together,  they  must 
possess  but  the  one  common  element,  C. 

2.  In  the  same  way  S,  may  resemble  S,,  in  more 
marks  than  merely  the  absence  of  C  and  so  for  any 
two  or  more  instances  in  the  series  S,,  S^p  S^^,  etc. 
However,  the  one  characteristic  common  to  them  all 
must  be  the  absence  of  C. 

3.  If  in  the  instances  chosen  an  element  is  com- 
mon to  all  in  addition  to  C,  or  in  the  second  set  its 
absence,  then  additional  instances  must  be  added  to 
the  tables  both  positive  and  negative  in  order  to 
secure  this  all-important  condition  of  elimination 
through  suitable  variation. 

4.  Moreover,  the  two  series,  positive  and  negative, 
must  have  their  settings  similar.  S,,  S,,,  8,^^,  etc., 
must  resemble  S',  S",  S'",  etc.  ;  otherwise  the  nega- 
tive instances  Avould  not  be  signihcant.     They  must 


120  INDUCTIVE  LOGIC 

be  chosen  from  the  same  sphere  as  the  positive,  that 
they  may  be  similar.  It  is  possible  to  multiply  neg- 
ative instances  ad  injinitum,  which,  however,  would 
furnish  no  ground  for  any  inference,  because  they 
would  be  wholly  irrelevant  to  the  problem  under 
investigation. 

5.  If  S^  is  so  similar  to  S'  as  to  be  identical  with 
it,  and  also  s,  pass  over  into  s' ;  then  we  have  the 
method  of  difference  in  its  pure  form :  — 

JS'+C s'  +  e 

S' s' 

Here  the  setting,  instead  of  being  similar  in  the  two 
cases,  is  the  same  in  each. 

The  following  is  an  experiment  of  Sir  John  Lub- 
bock's concerning  the  sense  of  smell  in  insects,  which 
I  have  chosen  as  illustrating  this  method  of  induc- 
tive research.  He  took  a  large  ant  and  tethered 
her  on  a  board  by  a  thread.  When  she  was  quite 
still,  he  brought  a  tuning-fork  into  close  proximity 
to  her  antennae,  but  she  was  not  disturbed  in  the 
least.  He  then  approached  the  feather  of  a  pen 
very  quietly,  so  as  almost  to  touch  first  one  and 
then  the  other  of  the  antennse,  which,  however,  did 
not  move.  He  then  dipped  the  pen  in  the  essence 
of  musk  and  did  the  same  ;  the  antenna  was  slowly 
retracted  and  drawn  quite  back.  He  then  repeated 
the  same  with  the  other  antenna,  and  with  like 
result.  Care  was  taken  throughout  not  to  touch 
the  antennge.  Lubbock  then  repeated  the  experi- 
ment with  a  number  of  different  ants,  and  using 
various  substances.     The  results  in  all  cases  were 


METHOD  OF  AGREEMENT  AND  DIFFERENCE      121 

the  same,  and  tlie  inference  was  naturally  drawn 
that  the  antennae  possessed  the  sense  of  smell.  In 
these  experiments,  various  substances  were  taken 
having  nothing  in  common  save  the  odor  of  musk 
that  had  been  placed  upon  them. 

In  some  cases  it  is  not  possible  to  discover  posi- 
tive instances  in  which  the  only  common  element 
is  the  suspected  cause.  In  such  cases  the  method 
is  not  conclusive  in  its  results,  although  it  may 
attain  a  high  degree  of  probability,  if  all  the  com- 
mon elements  save  the  suspected  cause-element 
are  known  to  be  irrelevant,  or  can  in  any  other  way 
be  proved  to  have  no  influence  whatsoever  upon  the 
result.  For  instance,  an  illustration  is  often  given 
of  this  method,  which  fails  in  the  manner  just  de- 
scribed. A  man  is  attempting  to  discover  whether 
a  particular  article  of  food  disagrees  with  him. 
He  notices  several  occasions,  a  large  number  if 
you  please,  when  he  has  eaten  this  particular  kind 
of  food,  and  has  soon  after  experienced  distress. 
These  are  the  positive  instances.  This  peculiar 
distress  has  never  been  experienced  when  he  has 
abstained  from  the  food  in  question.  The  inference 
is  that  this  food  has  caused  the  distress.  In  the 
various  instances,  however,  the  sole  element  in 
common  is  not  merely  the  taking  or  not  taking  the 
food.  The  person's  whole  bodily  organism  is  com- 
mon to  all  the  instances.  Within  it,  unforeseen 
complications  independent  of  this  article  of  food 
might  have  caused  the  trouble.  In  such  cases, 
number  of  instances  must  be  resorted  to  in  order  to 
render  the  possibility  of  a  coincidence  impossible. 


122  INDUCTIVE  LOGIC 

So  also  in  such  cases  as  the  treatment  of  any  given 
disease  in  a  hospital  An  experiment  may  be  tried 
in  the  treatment,  say,  of  typhoid  fever.  One  ward 
may  be  subjected  to  a  particuhar  kind  of  treatment, 
and  another  ward  not  subjected  to  that  treatment. 
If  recovery  is  hastened  in  the  one  and  retarded 
in  the  other  case,  an  inference  may  be  drawn  as 
to  efficacy  of  this  treatment.  In  these  instances 
again,  while  they  are  all  different  patients,  still  the 
nursing,  surroundings,  etc.,  are  common  to  them 
all.  It  must  be  shown  that  these  are  present 
both  in  the  negative  and  positive  instances,  and 
equally  capable  of  accomplishing  the  effect  if  they 
had  been  real  causes.  They  may  therefore  be 
eliminated  in  comparing  the  two  sets  of  instances, 
because  common  both  to  the  negative  and  positive 
cases.  In  this  also  resort  must  be  had  to  the  num- 
ber of  instances  in  order  to  eliminate  chance  coin- 
cidences. The  presence  of  common  elements  in 
excess  of  the  common  causal  element  may  be  rej)- 
resented  according  to  the  symbolical  notation  of 
the  joint  method,  by  the  introduction  of  another 
symbol  x.  Let  x  stand  for  that  which  is  common 
to  all  instances  in  addition  to  the  common  element 
C.     We  then  have :  — 

I.    Set  of  positive  instances. 

>S     -j-C-^x s    4-  e 

S'    -^  C-\-x s'  +e 

>S"  +  C  +  x s'  +e 

S<"  +  C-\-x s"'-\-e 

etc.  etc. 


METHOD   OF   AGREEMENT   AND  DIFFERENCE      123 

.  II.    Set  of  negative  instances. 

S,    -^x s, 

S,,   -^x Si/ 

Su,+^ ^"' 

etc.  etc. 

We  observe  x  in  all  instances  both  positive  and 
negative.  Being  present  when  the  effect  occurs 
and  when  it  does  not,  indifferently,  we  can  at  once 
infer  that  x  is  not  the  Avhole  cause  of  e.  However, 
it  may  have  united  with  C  in  the  first  set  of  instances 
to  produce  the  effect  e,  so  that  C  without  x,  or  some 
part  or  parts  of  x,  could  not  alone  produce  the  effect 
e.  In  all  such  cases  the  exact  force  of  x  must  be 
estimated  in  some  other  way.  If  x  is  extremely 
complex,  or  subject  to  change  from  forces  emanating 
from  within  itself,  as  in  the  case  of  organic  phenom- 
ena, then  it  becomes  extremely  difficult  to  determine 
X ;  and  consequently  the  method  of  agreement  and 
difference  does  not  yield  as  exact  results.  As  long 
as  the  force  of  x  remains  unknown,  it  becomes  the 
source  of  possible  disturbance,  which  may  wholly 
vitiate  the  results  attained. 

Mr.  Darwin,  in  his  experiments  upon  cross  and 
self  fertilization  in  the  vegetable  kingdom,  placed 
a  net  about  one  hundred  flower  heads,  thus  protect- 
ing them  from  the  bees  and  from  any  chance  of 
fertilization  by  means  of  the  pollen  conveyed  to 
them  by  the  bees.  He  at  the  same  time  placed  one 
hundred  other  flower  heads  of  the  same  variety  of 
plant  where  they  would  be  exposed  to  the  bees,  and, 
as  he  observed,  were  repeatedly  visited  by  them. 


124  INDUCTIVE  LOGIC 

Here  we  have  the  two  sets  of  instances,  in  one  the 
flowers  accessible  to  the  bees,  and  in  the  other,  not 
accessible.  He  obtained  the  following  result.  The 
protected  flowers  failed  to  yield  a  single  seed.  The 
others  produced  68  grains  weight  of  seed,  which  he 
estimated  as  numbering  2720  seeds.  Cross-fertiliza- 
tion as  the  cause  in  this  case  is  thus  proved.  The 
common  element  in  all  these  instances,  however,  is 
not  merely  the  presence  in  one  case  and  the  absence 
in  the  other  of  the  bees ;  there  is  also  the  element 
of  the  common  plant  structure  running  through  all  of 
the  two  hundred  instances.  This  element  is,  how- 
ever, of  such  an  unvarying  nature  in  all  the  instances, 
and  the  number  observed  so  many  as  to  eliminate 
the  possibility  of  any  given  plant  structure  possess- 
ing unobserved  peculiarities  suflicient  to  produce  the 
result  in  question.  It  may  therefore  be  considered 
as  an  inert  element  as  regards  the  effects  noticed  in 
the  one  and  absent  in  the  other  set  of  instances. 

Sir  John  Lubbock,  in  his  researches  concerning 
the  different  functions  of  the  two  kinds  of  eyes  in 
insects,  illustrates  the  joint  method  in  its  general 
features.  The  two  kinds  of  eyes  are  the  large  com- 
pound eyes,  situated  one  on  each  side  of  the  head, 
and  the  ocelli,  or  small  eyes,  of  which  there  are 
generally  three,  arranged  in  a  triangle  betAveen  the 
other  two.  He  wished  to  determine  the  precise 
function  of  the  small  eyes,  the  ocelli ;  and  he  has 
gathered  together  the  following  facts.  Plateau  has 
shown  that  caterpillars,  which  possess  ocelli,  but  no 
compound  eyes,  are  very  short-sighted,  not  seeing 
above  one  to  two  centimetres.     He  has  also  proved 


IVIETHOD  OF  AGREEMENT  AND  DIFFERENCE      125 

by  experiments  tliat  spiders,  which  have  ocelli  but 
no  compound  eyes,  are  very  short-sighted ;  they  were 
easily  deceived  by  artificial  flies  of  most  inartistic 
construction,  and  even  hunting   spiders  could  not 
see  beyond  ten  centimetres  (four  inches).     Lubbock 
experimented  on  this  point  with  a  female  spider, 
which,  after  laying  her  eggs,  had  rolled  them  into  a 
ball,  and  had  enveloped  the  whole  with  a  silken  bag 
which  she  carried  about  with  her.    Having  captured 
the  female  and  having  taken  the  bag  of  eggs  from 
her,  he  placed  it  on  a  table  about  two  inches  in 
front  of  her.     She  evidently  did  not  see  it.     He 
then  pushed  it  gradually  towards  her,  but  she  took 
no  notice  till  it  nearly  touched  her,  when  she  eagerly 
seized  it.     He  then  took  it  away  a  second  time,  and 
put  it  in  the  middle  of  the  table,  which  was  two 
feet  four  inches  by  one  foot  four,  and  had  nothing 
else  on  it.     The  spider  wandered  about  for  an  hour 
and  fifty  minutes  before  she  found  it,  apparently 
by  accident.     He  then  took  it  away  again  and  put 
it  down  as  before,  when  she  wandered  about  for  an 
hour  without   finding  it.     Like  experiments  were 
tried  with  other  spiders  and  with  the  same  results. 
Plateau  also  experimented  with   scorpions  which 
had  ocelli  and  no  compound  eyes.     They  appeared 
scarcely  to  see  beyond  their  own  pincers.     More- 
over, the  ocelli  are  especially  developed  in  insects, 
such  as  ants,  bees,  and  wasps,  which  live  partly  in 
the  open  light  and  partly  in  the  dark  recesses  of 
nests.     Again,  the  night-flying  moths   all  possess 
ocelli.     On  the  other  hand,  however,  they  are  en- 
tirely  absent    in    all    butterflies,    with,    according 


126  INDUCTIVE  LOGIC 

to  Scudder,  but  one  exception,  namely,  the  genus 
Pamphila.  Forel,  moreover,  varnished  the  com- 
pound eyes  of  various  insects  which  had  ocelli  as 
well.  The  latter,  however,  he  allowed  to  remain  in 
their  natural  state.  Inasmuch  as  their  habits  of 
flight  required  powers  of  vision  in  these  insects 
extending  to  a  considerable  distance,  it  happened 
that  when  placed  on  the  ground  they  made  no  at- 
tempt to  rise;  while,  if  thrown  into  the  air,  they 
flew  first  in  one  direction  and  then  in  another, 
striking  against  any  object  that  came  in  their  way, 
and  being  apparently  quite  unable  to  guide  them- 
selves. They  flew  repeatedly  against  a  wall,  falling 
to  the  ground,  and  unable  to  alight  against  it,  as 
they  did  so  cleverly  when  they  had  their  compound 
eyes  to  guide  them.  All  these  instances,  taken 
together  in  their  positive  and  negative  aspects,  led 
Sir  John  Lubbock  to  infer  that  the  ocelli  were  use- 
ful in  dark  places  and  for  near  vision,  while  the 
compound  eyes  were  for  the  light  and  more  distant 
vision.^ 

Another  illustration  of  this  method  may  be  found 
in  Darwin's  account  of  the  extreme  tameness  of  the 
birds  in  the  Galapagos  and  Falkland  islands.  I 
quote  some  extracts  from  his  narrative,  in  which  it 
will  be  seen  that  Darwin's  inferences  follow  from 
his  comparison  of  the  positive  and  negative  instances 
before  him.  He  says :  ''  This  tameness  of  dispo- 
sition is  common  to  all  the  terrestrial  species  of 
these  islands  in  the  Galapagos  Archipelago ;  namely, 

1  Lubbock,  On  the  Senses,  Instinct,  and  Intelligence  of  Ani- 
mals, pp.  175  ff. 


METHOD  OF  AGREEMENT   AND  DIFFERENCE      127 

to  the  mocking-tlirushes,  the  finches,  wrens,  tyrant 
flycatchers,  the  dove,  and  carrion-buzzard.  All  of 
them  often  approached  sufficiently  near  to  be  killed 
with  a  switch,  and  sometimes,  as  I  myself  tried, 
with  a  cap  or  hat.  A  gun  is  here  almost  super- 
fluous; for,  with  the  muzzle,  I  pushed  a  hawk  off 
the  branch  of  a  tree.  In  Charles  Island,  which  had 
been  colonized  about  six  years,  I  saw  a  boy  sitting 
by  a  well  with  a  switch  in  his  hand,  with  which  he 
killed  the  doves  and  finches  as  they  came  to  drink. 
He  had  already  procured  a  little  heap  of  them  for 
his  dinner ;  and  he  said  that  he  had  constantly  been 
in  the  habit  of  waiting  by  this  well  for  the  same 
purpose.  The  Falkland  Islands  offer  instances  of 
birds  with  a  similar  disposition.  The  snipe,  upland 
and  lowland  goose,  thrush  bunting,  and  even  some 
true  hawks,  are  more  or  less  tame.  The  black- 
necked  swan  is  here  wild,  and  it  was  impossible  to 
kill  it.  It,  however,  is  a  bird  of  passage,  which 
probably  brought  with  it  the  wisdom  learned  in 
foreign  countries. 

From  these  several  facts,  we  may,  I  think,  con- 
clude that  the  wildness  of  birds  with  regard  to 
man,  is  a  particular  instinct  directed  against  him 
and  not  dependent  on  any  general  degree  of  caution 
arising  from  other  sources  of  danger ;  secondly, 
that  it  is  not  acquired  by  individual  birds  in  a 
short  time,  even  when  much  persecuted,  but  that 
in  the  course  of  successive  generations  it  becomes 
hereditary.  With  domesticated  animals  we  are 
accustomed  to  see  new  mental  habits  or  instincts 
acquired  and  rendered  hereditary,  but  with  animals 


128  ixducti^t:  logic 

in  a  state  of  nature  it  must  always  be  most  difficult 
to  discover  instances  of  acquired  hereditary  knowl- 
edge. In  regard  to  the  wildness  of  birds  towards 
man,  there  is  no  way  of  accounting  for  it  except  as 
an  inherited  habit :  comparatively  few  young  birds, 
in  any  one  year,  have  been  injured  by  man  in 
England,  yet  almost  all,  even  nestlings,  are  afraid 
of  him ;  many  individuals,  on  the  other  hand,  both 
at  Galapagos  and  at  the  Falklands,  have  been  pur- 
sued and  injured  by  him,  but  yet  have  not  learned 
a  salutary  dread  of  him."  ^ 

I  have  given  this  quotation  somewhat  at  length 
in  order  to  show  the  method  of  a  great  investigator 
in  the  realm  of  nature;  and  that  it  may  be  seen 
how  naturally  he  falls  into  the  method  of  compar- 
ing positive  and  negative  sets  of  instances  relative 
to  the  object  of  research.  The  animal  and  vege- 
table kingdoms  are  especially  adapted  to  the  appli- 
cation of  this  joint  method,  and  therefore  it  is  in 
biology  that  it  is  most  frequently  employed  and 
where  it  has  yielded  the  most  fertile  results. 

The  advantage  of  the  joint  method  over  the  sim- 
ple method  of  agreement  is  that  it  largely  elimi- 
nates the  possibility  of  there  being  any  other  cause 
of  the  given  phenomenon  than  the  one  disclosed 
by  the  operation  of  this  method.  The  method  of 
agreement,  as  ^ve  have  seen,  often  fails  of  a  definite 
result  owing  to  the  plurality  of  causes.  The  joint 
method  tends  to  indicate  the  one  and  only  cause, 
and  when  the  instances  are  rigorously  selected  ac- 
cording to  the  conditions  of  the  canon,  there  is  a 

1  Darwin,  Voyage  of  a  Naturalist,  Vol.  II.  pp.  172  f. 


METHOD  OF   AGREEMENT  AND  DIFFERENCE      129 

high  degree  of  probability  that  the  sole  cause  is 
discovered.  Mr.  Mill  at  this  point  claims  too  much 
for  the  method  in  insisting  that  it  gives  a  certainty 
regarding  the  sole  cause,  when  the  requirements 
are  perfectly  realized.  It  is  impossible  to  realize 
the  requirements  perfectly.  In  selecting  the  nega- 
tive instances,  we  are  never  sure  that  we  have 
compassed  the  entire  sphere  of  significant  negative 
instances.  We  may,  however,  attain  results  highly 
probable  in  this  regard,  though  they  may  not  reach 
an  absolute  certainty.  Such  a  statement  is  more 
moderate  in  its  expression,  and  practically  it  assures 
as  satisfactory  results. 


CHAPTEE   X 

The  Method  of  Concomitant  Variations 

The  method  of  concomitant  variations  is  a 
process  of  determining  a  causal  relation  when,  as 
an  element  in  an  antecedent  varies  in  intensity, 
greater  or  less,  there  is  observed  a  corresponding 
or  concomitant  variation  in  the  consequent. 

Canon  of  the  3Iethod  of  Concomitant  Variations.  — 
Whatever  phenomenon  varies  in  any  manner,  when- 
ever another  phenomenon  varies  in  some  particular, 
is  either  a  cause  or  an  effect  of  that  phenomenon,  or 
is  connected  with  it  through  some  fact  of  causation. 

The  latter  clause  of  this  canon  provides  for  that 
circumstance  in  which  the  varying  elements  may 
both  be  concomitant  effects  of  a  common  cause. 
When  we  are  assured  of  the  absence  of  any  possi- 
ble common  cause  to  which  we  can  assign  the  two 
phenomena  as  effects,  then  they  must  be  related 
between  themselves  as  cause  and  effect.  A  simple 
illustration  of  this  method  is  the  rise  of  the  mer- 
cury in  the  thermometer  owing  to  the  increase  of 
heat ;  its  fall,  whenever  there  is  decrease  of  heat. 
One  varies  as  the  other  concomitantly,  and  we  infer 
a  causal  relation  that  we  at  once  proceed  to  gen- 
eralize without  hesitation. 
130 


METHOD  OF  CONCOMITANT  VARIATIONS       131 

The  symbolical  representation  of  this  method  is 
as  follows : — 

S-hC s  +  e 

JS-\-C±dC s-^e±de 

etc.  etc. 

Then  C  is  the  cause  of  e. 

I  have  used  clC,  and  cle  to  denote  the  increments 
or  decrements  of  the  cause  and  effect  respectively. 
This  method  is  used  generally  when  the  method  of 
difference  is  impossible,  owing  to  the  fact  that  the 
supposed  causal  element  cannot  be  made  to  vanish 
wholly.  In  all  such  cases  a  variation  of  the  ele- 
ment is  resorted  to,  and  the  corresponding  result 
observed.  Heat  is  relative  and  not  absolute,  as  also 
the  height  of  mercury  in  the  tube.  The  relation 
is  determined,  therefore,  by  variations,  greater  and 
less.  This  method  is  also  used  to  supplement  the 
results  of  other  methods  by  which  a  causal  relation 
has  been  determined,  but  not  in  exact  quantitative 
terms.  It  may  be  known  that  a  certain  phenome- 
non C  is  always  the  cause  of  a  certain  effect  e,  and 
the  method  of  concomitant  variations  will  then  be 
of  use  in  determining  precisely  how  much  of  a  vari- 
ation in  C  will  cause  a  specified  variation  in  e.  A 
law  finds  scientific  expression  only  when  stated  in 
terms  of  exact  quantitative  relation  betM^een  varia- 
tions in  antecedent  and  consequent.  We  may  ex- 
press the  law  of  universal  attraction  in  a  vague  way 
that  bodies  always  attract  each  other  and  the  greater 
attraction  when  the  bodies  are  nearer  together,  and 
the  larger  they  are.     But  this  statement  needs  to 


132  INDUCTR^E  LOGIC 

be  recast  in  terms  exhibiting  the  precise  quantita- 
tive variation.  Bodies  attract  each  other  directly 
as  the  product  of  their  masses,  and  inversely  as  the 
square  of  their  distance.  It  is  evident  that  the 
special  function  of  this  method  of  concomitant  vari- 
ations consists  in  just  this  quantitative  determina- 
tion. In  one  respect,  therefore,  it  may  be  regarded 
as  a  substitute  for  the  method  of  difference,  and 
in  another  way  as  a  supplement  to  the  method  of 
difference  in  leading  to  quantitatively  determinate 
results. 

The  quantitative  variation  between  antecedent 
and  consequent  may  be  either  direct  or  inverse  vari- 
ation. The  former  is  when  one  increases  as  the 
other  increases,  or  when  one  decreases  as  the  other 
decreases.  The  inverse  is  when  one  decreases  as  the 
other  increases,  or  vice  versa.  This  may  be  expressed 
symbolically 

S-Y-C±dG    .     .     .     .     s-^eTde 

We  have,  for  instance,  Boyle's  law  as  regards  the 
variation  of  volume  of  gases  according  to  the  press- 
ure; that  is,  when  we  double  the  pressure,  we  halve 
the  volume.  This  may  be  proved  experimentally. 
The  method  also  was  used  by  Ricardo  to  prove  his 
law  that  the  rate  of  profits  varies  in  inverse  ratio  to 
the  rate  of  wages.  We  have  also  the  tendency  ob- 
served in  respect  to  increase  of  crimes,  when  there 
is  decrease  of  opportunities  for  labor. 

The  expression  of  a  law  in  terms  of  the  quantita- 
tive relation  between  antecedent  and  consequent 
may  be  facilitated  by  a  graphic  representation  of  the 


METHOD  OF  CONCOMITANT  VARIATIONS       133 

sa^ne,  tliroiigh  corresponding  abscissae  and  ordinates. 
The  varying  antecedents,  for  instance,  may  be  laid 
off  on  the  axis  of  X,  and  each  several  consequent 
represented  by  the  corresponding  ordinates.  The 
resulting  curve  thus  obtained  will  represent  the  law 
of  their  mutual  relation.  If  the  equation  of  the 
curve  can  be  determined,  it  will  represent  the  math- 
ematically exact  expression  of  the  law  in  question. 
If  this  is  not  possible,  it  may  prove  at  least  sug- 
gestive of  the  law  which  otherwise  might  have 
remained  concealed.  This  graphical  method  is 
especially  useful  in  dealing  with  physical  phenom- 
ena. "  If  the  abscissae  represent  intervals  of  time, 
and  the  ordinates  corresponding  height  of  the  ba- 
rometer, we  may  construct  curves  which  show  at  a 
glance  the  dependence  of  barometric  pressure  upon 
the  time  of  day.  Such  curves  may  be  accurately 
drawn  by  photographic  processes  on  a  sheet  of  sen- 
sitive paper  placed  behind  the  mercurial  column, 
and  made  to  move  past  it  with  a  uniform  horizontal 
velocity  by  clockwork.  A  similar  process  is  applied 
to  the  temperature  and  electricity  of  the  atmosphere, 
and  to  the  components  of  terrestrial  magnetism."  ^ 

This  method,  moreover,  has  the  advantage  of  the 
psychological  impression  which  it  makes.  The 
mind  is  more  susceptible  to  the  perception  of  varia- 
tion in  forces  where  the  change  is  apparent  to  the 
senses,  than  to  the  perception  of  a  constant  force, 
whose  constant  character  thereby  conceals  its  nat- 
ure  and  function  from  the  senses.      Synchronous 

1  Thomson  and  Tait,  Elements  of  Natural  Philosophy ,  Vol. 
I.  p.  119. 


134  INDUCTIYE  LOGIC 

changes  attract  the  attention,  and  admit  of  ready 
comparison,  as  we  follow  out  the  variations  from 
point  to  point.  We  may  ring  a  bell  in  a  vacuum, 
and  detect  no  sound  whatsoever,  and  then  allow  the 
air  to  enter  gradually.  We  notice  that  as  the  air 
enters  more  and  more  freely,  the  sound  grows 
louder  and  louder.  The  relation  of  cause  and  effect 
is  thus  demonstrated  to  the  senses  in  the  most  vivid 
manner  possible.  The  variations  are  exhibited  side 
by  side,  and  thus,  presented  together  in  their  con- 
comitant relation,  produce  the  deeper  impression. 

This  method  is  of  special  advantage  in  all  experi- 
ments where  the  intensity  of  the  forces  can  be 
varied  at  will  and  the  consequent  effects  exhibited 
in  some  palpable  manner.  The  determination  of 
the  heat  rays  in  the  solar  spectrum  is  accomplished 
by  this  method.  The  spectrum  may  be  received 
upon  a  plate  pierced  with  a  narrow  slit,  through 
which  the  rays  can  act  upon  a  thermo-electric  pile, 
which  will  indicate  by  deflections  of  a  needle  the 
varying  intensity  of  the  heat  in  the  several  rays  of 
the  spectrum.  Now,  move  the  slit  through  the 
whole  extent  of  the  spectrum,  beginning  with  the 
violet  portion.  AVhile  in  the  violet,  the  indigo, 
the  blue,  and  even  the  green,  the  needle  of  the  ther- 
moscopic  apparatus  will  be  deflected  but  slightly, 
it  will  indicate  an  amount  of  heat  increasing  as 
the  slit  crosses  the  yellow,  next  the  orange,  then 
the  red ;  and  then  beyond  the  red,  and  entering  the 
dark  portion  of  the  spectrum,  we  find  the  greatest 
deflection  of  all.  The  maximum  of  heat  is  there- 
fore  in  a  region   beyond   the   observation  of   the 


METHOD  OF  CONCOMITANT   VARIATIONS       135 

senses  when  unaided  by  experimental  device ;  and 
yet  revealed  conclusively  by  this  method.^ 

Professor  Tyndall  performed  a  very  interesting 
experiment  to  prove  that  the  cloud  of  darkness  sur- 
rounding flames  of  great  heat  was  due  to  the  fact 
that  the  heat  consumed  the  floating  motes  in  the 
air  which  serve  to  scatter  the  light  which  is  visible 
only  when  thus  diffused.  The  phenomenon  which 
he  endeavored  to  explain  was  somewhat  as  follows : 
Beneath  a  beam  of  electric  light,  a  red-hot  poker 
was  placed,  and  from  it  black  wreaths  as  of  smoke 
were  seen  to  ascend.  A  large  hydrogen  flame  being 
employed,  it  produced  whirling  masses  of  darkness 
far  more  copiously  than  the  poker.  Of  this  Pro- 
fessor Tyndall  remarked :  "  Smoke  was  out  of  the 
question ;  what  then  was  the  blackness  ?  It  was 
simply  that  of  stellar  space ;  that  is  to  say,  blackness 
resulting  from  the  absence  from  the  track  of  the 
beam  of  all  matter  competent  to  scatter  its  light. 
When  the  flame  was  placed  below  the  beam,  the  float- 
ing matter  was  destroyed  in  situ;  and  the  air  freed 
from  this  matter  rose  into  the  beam,  jostled  aside 
the  illuminated  particles,  and  substituted  for  their 
light  the  darkness  due  to  its  own  perfect  transpar- 
ency. Nothing  could  more  forcibly  illustrate  the 
invisibility  of  the  agent  which  renders  all  things 
visible.  The  beam  crossed,  unseen,  the  black  chasm 
formed  by  the  transparent  air,  w^hile  at  both  sides 
of  the  gap  the  thick-strewn  particles  shone  out  like 
aluminous  solid  under  the  powerful  illumination."^ 

1  Saigey,  The  Unity  of  Natural  Phenomena,  p.  61. 

2  Tyndall,  Fragments  of  Science,  p.  280. 


136  IXDUCTIVE  LOGIC 

Such,  being  the  phenomenon  and  Professor  TyndalPs 
explanation,  it  will  be  seen  that  he  proceeded  accord- 
ing to  the  method  of  concomitant  variations  in  the 
following  experiment  of  many  which  he  performed 
to  substantiate  this  theory  :  — 

A  platinum  tube,  with  its  plug  of  platinum 
gauze,  was  connected  with  an  experimental  tube, 
through  which  a  powerful  beam  could  be  sent 
from  an  electric  lamp  placed  at  its  end.  The 
platinum  tube  was  heated  till  it  glowed  feebly 
but  distinctly  in  the  dark.  The  experimental  tube 
was  then  exhausted,  and  filled  with  air  that  had 
passed  through  the  red-hot  tube.  A  considerable 
amount  of  floating  matter  which  had  escaped  com- 
bustion was  revealed  by  the  electric  beam. 

Then  the  tube  was  raised  to  a  brighter  redness 
and  the  air  permitted  to  pass  slowly  through  it. 
Though  diminished  in  quantity,  a  certain  amount 
of  floating  matter  passed  into  the  exhausted  ex- 
perimental tube. 

The  platinum  tube  was  rendered  still  hotter;  a 
barely  perceptible  trace  of  the  floating  matter  now 
passed  through  it.  The  experiment  was  repeated, 
with  the  difference  that  the  air  was  sent  more 
slowly  through  the  red-hot  tube.  The  floating 
matter  was  totally  destroyed. 

The  platinum  tube  was  now  lowered  until  it 
bordered  upon  a  visible  red  heat.  The  air,  sent 
through  it  still  more  slowly  than  in  the  last  ex- 
periment, carried  with  it  a  cloud  of  floating  mat- 
ter. Professor  Tyndall's  commentary  upon  this 
experiment    is    as    follows :    "  If,    then,    the    sus- 


METHOD  OF  CONCOMITANT   VARIATIONS       137 

pended  matter  is  destroyed  by  a  bright  red  heat, 
much  more  is  it  destroyed  by  a  flame,  whose  tem- 
perature is  vastly  higher  than  any  employed  in 
this  experiment.  So  that  the  blackness  intro- 
duced into  a  luminous  beam  where  a  flame  is 
placed  beneath  it  is  due,  as  stated,  to  the  destruc- 
tion of  the  suspended  matter."  ^ 

Professor  Tyndall  also  supplemented  this  experi- 
ment by  one  which  was  according  to  the  joint 
method  of  agreement  and  difference.  He  prepared 
oxygen  so  as  to  exclude  all  floating  particles,  and 
found  that  when  blown  into  the  beam,  darkness 
was  produced ;  also  that  hydrogen,  nitrogen,  car- 
bonic acid,  and  coal-gas,  when  prepared  in  a  similar 
way,  each  produce  darkness  when  poured  or  blown 
into  the  beam.  These  instances,  combined  with 
various  positive  instances  of  illumination  of  mote- 
strewn  currents  of  air,  illustrate  the  method  of 
agreement  and  difference. 

An  additional  experiment,  according  to  the  method 
of  difference,  was  as  follows :  Professor  Tyndall 
placed  an  ordinary  glass  shade  in  the  air  with  its 
mouth  downward.  This  permitted  the  track  of  the 
beam  to  be  seen  crossing  it.  Letting  coal-gas,  or 
hydrogen,  enter  the  shade  by  a  tube  reaching  to 
its  top,  the  gas  gradually  filled  the  shade  from  the 
top  downward.  As  soon  as  it  occupied  the  space 
crossed  by  the  beam,  the  luminous  track  was  in- 
stantly abolished.  Lifting  the  shade  so  as  to  bring 
the  common  boundary  of  gas  and  air  above  the 
beam,  the  track  flashed  forth.    After  the  shade  was 

1  Tyndall,  FragmeiUti  of  Science,  pp.  283,  284. 


138  INDUCTR^  LOGIC 

full,  he  inverted  itj  thereupon  the  gas  passed  up- 
ward like  a  black  smoke  among  the  illuminated 
particles.^ 

The  method  of  concomitant  variations  is  not 
only  capable  of  illustration  by  laboratory  methods 
and  devices ;  it  finds  abundant  illustration  as  well 
in  the  realm  of  nature,  Avhere  observation  alone 
becomes  the  instrument  of  investigation  and  Avhere 
experiment  is  impossible  or  impracticable.  Lyell, 
in  his  Principles  of  Geology,  gives  a  very  interest- 
ing account  of  the  alternate  elevation  and  subsi- 
dence of  the  temple  of  Jupiter  Serapis,  at  Pozzuoli, 
on  the  Bay  of  Naples.^  It  is  situated  in  proximity 
to  several  volcanoes,  Vesuvius,  however,  being  at 
some  distance.  It  has  been  observed  that  there  is 
a  certain  connection  between  each  era  of  upheaval, 
and  a  local  development  of  volcanic  heat;  and  on 
the  other  hand,  between  each  era  of  depression,  and 
the  local  quiescent  condition  of  volcanic  phenomena. 
Before  the  Christian  era,  when  Ischia  was  in  a  state 
of  eruption,  and  Avernus  and  other  points  in  the 
Phlegrsean  fields  were  celebrated  for  their  volcanic 
character,  it  was  observed  that  at  that  time  the 
ground  on  which  the  temple  stood  was  several  feet 
above  water.  Vesuvius  was  then  regarded  as  a  spent 
volcano.  After  the  Christian  era,  Vesuvius  became 
active  and  then  scarcely  a  single  eruption  occurred 
in  Ischia  or  around  the  Bay  of  Baise.  It  was  ob- 
served that  at  that  time  the  temple  was  sinking. 
Vesuvius  then  became  quiet  for  five  centuries  pre- 

1  Tyndall,  Fragments  of  Science,  pp.  284,285. 

2  Chapter  XXX. 


METHOD  OF  CONCOMITANT  VARIATIONS       139 

ceding  the  eruption  of  1631,  and  during  that  period 
the  Solfatara  was  in  eruption  in  1198,  Ischia  in  1302, 
and  Monte  Nuovo  was  formed  in  1538.  Then  the 
foundations  of  the  temple  were  observed  to  be  ris- 
ing again.  Vesuvius  became  active  after  that,  and 
has  continued  so  ever  since,  and  during  this  time 
the  temple  has  been  subsiding.  The  inference  is 
that  as  the  subterranean  heat  increases,  and  lava 
forming  without  obtaining  an  easy  vent  like  that 
afforded  by  Vesuvius,  the  surface  is  elevated,  but 
when  the  rocks  below  are  cooling  and  contracting, 
the  pent-up  fire  being  withdrawn  in  the  eruption  of 
the  great  Vesuvius,  then  there  is  a  corresponding 
subsidence. 

The  observation  of  concomitant  variations  is 
furthermore  illustrated  in  Darwin's  researches  con- 
cerning the  formation  of  coral  reefs,  as  regards  the 
question  which  some  naturalists  have  raised  as  to 
which  part  of  the  coral  reef  is  most  favorable  to  the 
growth  of  coral. ^  He  adduces  the  following  facts, 
most  of  which  are  the  direct  result  of  his  observa- 
tions :  "  The  great  mounds  of  living  Porites  and  of 
Millepora  round  Keeling  atoll  occur  exclusively 
on  the  extreme  verge  of  the  reef,  which  is  washed 
by  a  constant  succession  of  breakers.  At  the  Mar- 
shall Islands  the  larger  kinds  of  coral  which  form 
rocks  measuring  several  fathoms  in  thickness  pre- 
fer the  most  violent  surf.  The  outer  margin  of  the 
Maldiva  atolls  consists  of  living  corals,  and  here 
the  surf  is  so  tremendous  that  even  large  ships 
have  been  thrown,  by  a  single   heave  of   the  sea, 

1  Darwin,  Coral  Reefs,  pp.  87  f . 


140  INDUCTIVE  LOGIC 

high  and  dry  on  the  reef,  all  on  board  thus  escap- 
ing with  their  lives.  In  the  Red  Sea  the  strongest 
corals  live  on  the  outer  reefs  and  appear  to  love  the 
surf.  From  these  facts  it  is  certain  that  the  strong- 
est and  most  massive  corals  flourish  where  most 
exposed.  The  less  perfect  state  of  the  reef  of  most 
atolls  on  the  leeward  and  less  exposed  side,  com- 
pared with  its  state  to  the  windward,  and  the  anal- 
ogous case  of  the  greater  number  of  breaches  on  the 
rear  sides  of  those  atolls  in  the  Maldiva  Archipelago, 
which  afford  some  protection  to  each  other,  are  obvi- 
ously explained  by  this  circumstance."  There  seems 
to  be  here  a  combination  of  the  method  of  agree- 
ment with  that  of  concomitant  variations.  And 
such  a  combination  may  be  employed  to  advantage 
in  cases  where  the  phenomena  under  investigation 
show  forces  under  varying  degrees  of  intensity; 
the  causal  relation  is  more  apparent,  and  the  pos- 
sibility of  fortuitous  coincidence  is  largely  elimi- 
nated if  a  number  of  instances  can  be  collected 
in  which  the  forces  manifest  themselves  in  var}^- 
ing  degrees.  Accumulation  of  instances,  showing 
concomitant  variations  in  the  forces  observed,  cor- 
responds to  the  actual  variations  which  in  an  experi- 
ment are  effected  by  the  investigator  himself.  In 
such  observed  instances,  however,  we  cannot  always 
have  before  us  the  variations  expressed  continuously. 
There  are  evident  gaps  that  must  be  interpolated 
mentally.  In  the  experiment,  however,  of  whatever 
nature,  the  degrees  of  intensity  can  be  exhibited 
continuously,  one  degree  merging  into  another 
through  inapi)reciable   increments.     There  is  thus 


METHOD  OF  CONCOMITANT  VAKIATIONS       141 

a  gradation  which  has  no  gaps  to  be  filled,  and  the 
psychological  impression  is  thereby  heightened. 

By  the  method  of  concomitant  variations  it  is 
possible  also  to  represent  to  the  mind  the  magni- 
tude of  an  unknown  force,  or  unobservable  force 
by  comparison  with  the  intensity  of  a  known  force, 
which  lies  within  the  sphere  of  observation.  For 
instance,  Mr.  Darwin  gives  an  interesting  account 
in  his  narrative  of  the  finding  near  the  shores  of 
the  Plata  a  group  of  vitrified  silicious  tubes  which 
had  been  formed  by  lightning  entering  loose  sand. 
The  internal  surface  of  such  tubes  is  completely  vit- 
rified, glossy,  and  smooth,  and  the  tubes  themselves 
are  generally  compressed,  and  have  deep  longitu- 
dinal furrows  so  as  closely  to  resemble  a  shrivelled 
vegetable  stalk,  or  the  bark  of  an  elm  or  cork  tree. 
Their  circumference  is  about  two  inches,  but  in 
some  fragments  which  are  cylindrical  and  without 
any  furrows,  it  is  as  much  as  four  inches.  Judging 
from  the  uncompressed  fragments,  the  measure  or 
bore  of  the  lightning  proved  to  be  about  one  inch 
and  a  quarter.  In  contrast  with  the  force  of  light- 
ning as  thus  revealed  in  its  effects,  Mr.  Darwin  cites 
some  experiments  performed  in  Paris  by  an  artifi- 
cial force  of  great  magnitude  indeed  and  yet  with 
results  that  seem  insignificantly  small  in  compari- 
son. He  says:  "At  Paris,  M.  Hatchette  and  M. 
Beudant  succeeded  in  making  tubes  in  most  respects 
similar  to  these  fulgurites  by  passing  very  strong 
shocks  of  galvanism  through  finely  powdered  glass  : 
they  failed,  however,  both  with  powdered  felspar 
and  quartz.     One  tube,  formed  with  pounded  glass, 


142  INDUCTIVE  LOGIC 

was  very  near  an  inch  long,  namely,  .982,  and  had 
an  internal  diameter  of  .019  of  an  inch.  When  we 
hear  that  the  strongest  battery  in  Paris  was  used, 
and  that  its  power  on  a  substance  of  such  easy  fusi- 
bility as  glass  was  to  form  tubes  so  diminutive,  we 
must  feel  greatly  astonished  at  the  force  of  a  shock 
of  lightning,  which,  striking  the  sand  in  several 
places,  has  formed  cylinders  in  one  instance  at  least 
thirty  feet  long,  and  having  an  internal  bore,  where 
not  compressed,  of  full  an  inch  and  a  half ;  and 
this  in  a  material  so  extraordinarily  refractory  as 
quartz  ! "  ^ 

The  method  of  concomitant  variations  may  be 
used  in  regard  to  phenomena  whose  nature  is  such 
as  seemingly  to  indicate  a  constant  law  of  variation, 
and  yet  inferences  based  thereupon  lead  to  false 
results.  It  is,  therefore,  well  to  note  some  of  these 
instances  by  way  of  general  precaution  in  applying 
this  method. 

1.  It  does  not  necessarily  follow  that  having 
observed  two  forces  varying  in  a  constant  ratio 
through  several  concomitant  modifications,  the 
same  ratio  will  be  preserved  indefinitely  through 
all  subsequent  changes.  Water  contracts  as  it  is 
cooling.  Suppose  we  begin  to  note  this  continued 
contracting  of  water  from  100°  F.  to  90° ;  we  natu- 
rally expect  to  find  it  continuing  through  90°  to  80°. 
And  as  we  observe,  we  find  our  expectations  con- 
firmed. And  so  on  through  to  40°,  we  find  that 
water  continues  to  contract.  It  is,  therefore,  most 
natural  for  us  to  expect  to  find  water  contracting 

1  Dai'wiu,  Voyage  of  a  Naturalist,  Vol.  I.  pp.  76  f. 


METHOD  OF  CONCOMITANT  VARIATIONS       143 

at  39°.  But  just  at  this  point  in  the  series,  there  is 
a  break  in  the  continuity  of  variation ;  at  39°  water 
begins  to  expand  and  so  continues  until  it  passes  into 
the  solid  form  at  the  freezing-point.  The  same  also 
is  illustrated  in  Weber's  law,  already  mentioned, 
which  expresses  the  quantitative  relation  between 
the  stimulus  and  the  corresponding  sensation.  The 
law  is  that  the  force  of  the  stimulus  must  increase 
geometrically,  in  order  that  the  intensity  of  the 
sensation  should  increase  arithmetically.  This  law, 
however,  breaks  down  towards  the  upper  or  lower 
limits,  with  a  stimulus  of  slight  degree  of  intensity 
and  with  one  of  extreme  intensity.  We  find  also 
an  increase  of  temperature  as  we  proceed  towards 
the  centre  of  the  earth  of  about  one  degree  to 
every  fifty-three  feet  of  descent.  This  by  no  means 
warrants  us  in  inferring  that  this  ratio  continues 
constant  to  the  very  centre  itself.  In  certain 
phenomena,  moreover,  there  are  natural  limits,  as 
in  sound,  for  example,  where  the  pitch  rises  as  the 
number  of  vibrations  increases.  At  a  certain  point, 
varying  according  to  different  individuals,  increase 
of  vibrations  gives  no  resulting  sound  whatsoever ; 
and  so  there  is  a  lower  limit,  vibrations  may 
decrease  to  a  point  beyond  which  no  sound  is 
heard. 

An  illustration  of  this  fallacy,  though  not  strictly 
of  the  method  of  concomitant  variations,  is  given 
by  Jevons.  He  takes  the  following  series  of  prime 
numbers:  41,  43,  47,  53,  61,  71,  83,  97,  113,  131, 
etc.  It  will  be  seen  that  they  all  agree  in  being 
values    of    the    general    expression    x^  -\-  x  -\-  41^ 


144  INDUCTIVE  LOGIC 

where  we  put  for  x  the  successive  vahies  of  0,  1, 
2,  3,  4,  etc.  For  instance,  let  x  =  ()  in  x' -{- x -{■ 
41,  we  get  41 ;  let  x  =  1  in  the  same,  we  get  43 ; 
when  X  =  2,  we  get  47 ;  and  so  on.  It  seems  as 
though  we  could  keep  this  up  indefinitely,  2:)roduc- 
ing  an  increasing  series,  always  of  prime  numbers. 
It  is  found,  however,  that  if  we  take  x  =  40,  in 
the  formula  x^  +  x-\-'il,  we  shall  have  40  x  40 
4-  40  -f  41,  which  equals  1681,  and  this  number  is 
the  square  of  41  and  therefore  not  a  prime  number. 
At  this  point  the  law  breaks  down.^ 

In  the  sphere  of  political  economy  also  we  might 
be  led  into  an  easy  yet  false  inference.  Suj^pose 
a  certain  farm  yield  500  bushels  of  corn  with  a 
given  amount  of  expenditure  and  labor.  We  might 
think  that  if  we  doubled  the  expenditure  and 
labor,  we  will  also  be  able  to  double  the  results, 
and  obtain  a  yield  of  1000  bushels  as  over  against 
the  500  of  the  previous  year.  Here,  however,  what 
is  known  as  the  law  of  decreasing  returns  obtains ; 
to  double  the  product  it  may  be  necessary  to  triple 
or  quadruple  the  labor  and  expense.  "  Thus  in  the 
production  of  any  plot  of  land  there  is  a  point  of 
equilibrium,  which  marks  an  impassable  limit,  not 
of  course  a  limit  which  could  not  be  passed  if  it 
were  wished,  but  one  that  no  one  wishes  to  pass, 
because  there  is  nothing  to  be  gained  by  so  doing."  - 

To  know  that  such  false  inferences  are  at  least 
possible  in  the  application  of  this  method  of  con- 
comitant variations  to  the  unknown  regions  beyond 

1  Jevons,  Principles  of  Science,  p.  230. 

2  Gide,  Political  Economy,  p.  325. 


METHOD  OF  CONCOMITANT  VARIATIONS       145 

our  experience,  may  serve  at  least  to  keep  us  on 
guard  under  similar  circumstances. 

2.  There  are  certain  phenomena,  moreover,  in 
which  an  increased  intensity  of  the  force  in  ques- 
tion may  give  rise  to  incidental  effects  Avhich  tend 
to  neutralize  the  chief  effect  to  be  attained.  For 
instance,  an  overdose  of  arsenic  causes  violent 
contractions  of  the  stomach  so  that  its  contents 
are  immediately  ejected,  and  thus  the  system  is 
relieved  of  the  noxious  substance. 

3.  Two  elements  in  a  given  phenomenon  may 
vary  together  constantly  and  yet  they  may  not  be 
related  at  all  as  cause  and  effect,  but  appear  as  coin- 
cidental effects  of  one  and  the  same  cause.  It  has 
been  observed  that  the  occurrence  of  the  Aurora 
Borealis  has  been  accompanied  by  pronounced  mag- 
netic disturbances.  It,  however,  cannot  be  inferred 
that  the  former  has  been  the  cause  of  the  latter ; 
they  are  probably  the  varied  effects  of  some  widely 
operating  magnetic  force. 

The  precaution  above  mentioned  has  already  been 
referred  to  as  provided  for  in  the  canon  of  this 
method  which  states  that  the  observed  concomitant 
variation  may  indicate  not  always  a  direct  causal 
element  between  the  two  varying  elements,  but 
that  they  are  at  least  connected  with  the  phe- 
nomenon under  investigation  through  some  fact  of 
causation. 


CHAPTER  XI 
The  Method  of  Residues 

The  metliod  of  residues  consists  in  the  analysis 
of  a  given  phenomenon  based  upon  previous  induc- 
tions, through  which  it  has  been  determined  that 
certain  elements  in  the  antecedent  have  caused 
certain  elements  in  the  consequent ;  the  inference 
is  then  drawn,  that  the  remaining  elements  of  the 
antecedent  are  necessarily  the  cause  of  the  remain- 
der of  the  consequent.  It  is  a  method  of  elimina- 
tion of  the  known  relations  so  as  to  simplify  the 
complex  character  of  the  phenomenon  and  disclose 
the  relations  that  are  unknown  in  the  light  of  a 
causal  connection  which  we  are  constrained  to  be- 
lieve must  obtain. 

Tlie  Canon  of  the  Metliod  of  Residues.  —  Subduct 
from  any  phenomenon  such  part  as  is  known  by 
previous  inductions  to  be  the  effect  of  certain  ante- 
cedents, and  the  residue  of  the  phenomenon  is  the 
effect  of  the  remaining  antecedents. 

The  symbolical  representation  is  as  follows  :  — 

Given  S -i- C s+e 

If  it  is  known  that  there  exists  the  causal  relation 

>S' s, 

146 


THE  METHOD  OF  RESIDUES  147 

we  may  then  infer  that  C  is  the  cause  of  e.  In 
this  C  may  be  simple  or  complex ;  if  it  is  simple, 
the  causal  relation  established  is  expressed  in  its 
simplest  terms  and  is  therefore  a  determinate  result. 
If,  however,  the  residue  C  is  complex,  it  must  be 
reduced  by  experimental  analyis  to  its  simplest 
elements,  and  their  relation  to  the  elements  into 
which  e  can  be  analyzed  further  determined. 

The  most  striking  illustration  of  this  method,  and 
one  of  the  most  brilliant  achievements  of  science 
as  well,  is  the  discovery  of  the  planet  Neptune  by 
Adams  and  Le  Verrier,  working  on  the  problem  in- 
dependently and  reaching  the  same  result.  These 
astronomers  had  observed  certain  perturbations  in 
the  planet  Uranus.  It  did  not  keep  in  its  proper 
orbit  as  determined  by  their  mathematical  calcula- 
tions based  upon  the  presence  of  the  known  stellar 
bodies.  It  behaved  as  though  beyond  its  orbit  was 
an  outer  planet,  Avhose  presence  alone  could  account 
for  the  observed  perturbations.  Adams  and  Le 
Verrier  then  proceeded  to  calculate  the  exact  posi- 
tion of  such  a  disturbing  body  as  determined  by 
the  nature  and  magnitude  of  the  perturbations  of 
Uranus.  The  telescope  was  then  pointed  to  the 
exact  point  in  the  heavens,  as  thus  indicated,  and 
the  planet  Neptune  was  revealed  to  the  eye  accord- 
ing to  the  determination  of  far-reaching  prophecy, 
which  confidently  asserted  that  it  must  be  there. 

The  method  of  residues  is  really  a  deductive 
method  based  upon  the  law  of  sufficient  reason ;  so 
many  elements  on  the  one  hand  producing  so  many 
elements  on  the  other ;  if,  then,  a  part  of  the  former 


148  INDUCTIVE  LOGIC 

is  to  be  checked  off  as  cause  of  a  part  of  the  latter, 
then  the  remainder  on  one  hand  must  be  the  cause 
of  the  remainder  on  the  other.  This  is  pure  de- 
duction. For  we  ask,  Why  are  we  constrained  to 
account  for  the  remainder  on  one  side  by  the  re- 
mainder on  the  other  ?  The  only  possible  answer 
is  that  it  must  be  accounted  for  within  the  system 
to  which  it  is  referred ;  and  but  one  part  therein  is 
left  which  can  possibly  account  for  it,  because  all 
the  others  are  specihcally  determined  in  the  known 
effects  which  they  have  produced.  This  method, 
however,  has  a  proper  place  among  the  inductive 
methods,  inasmuch  as  it  is  based  on  previous  induc- 
tions, and  leads  to  investigations  that  can  be  prose- 
cuted only  by  the  various  inductive  processes  of 
experiment. 

AYhen  the  residue  of  the  antecedent  is  a  simple 
element,  and  no  other  possible  causal  element  can 
lie  concealed  from  our  observation,  then  the  infer- 
ence is  simple  and  conclusive.  A  difficulty,  how- 
ever, may  present  itself,  owing  to  the  fact  that  the 
residual  element  is  apt  to  be  complex  and  leave  the 
phenomenon  still  indeterminate,  or  there  may  be  a 
lurking  element  unnoticed  by  us  which  is  the  real 
cause  in  question.  The  function  of  this  method  is, 
therefore,  largely  suggestive.  It  says  the  effect  is 
not  wholly  accounted  for  by  the  known  causal  ele- 
ments ;  there  is  a  residue  unaccounted  for,  and  its 
cause  is  to  be  sought  in  the  residue  of  the  antece- 
dent, and  if  it  is  thought  that  the  whole  of  the 
antecedent  is  comprehended,  the  question  is  started, 
May  there  not  be  unobserved  circumstances  of  the 


THE   METHOD  OF  RESIDUES  149 

antecedent  that  further  experiment  will  be  calcu- 
lated to  reveal?  In  many  cases,  therefore,  this 
method  must  be  supplemented  by  some  other  ex- 
perimental method  in  order  to  secure  more  precise 
determination,  generally  the  method  of  difference. 
It  often  happens  in  investigations  in  chemistry, 
astronomy,  and  physics,  that  the  actual  phenomena 
vary  in  greater  or  less  degree  from  their  expected 
behavior  according  to  established  theory.  This 
must  lead  either  to  a  reconstruction  of  theory,  or 
to  a  search  for  some  unobserved  force  sufficient  to 
account  for  the  discrepancy.  Herschel  was  the 
first  to  point  out  the  significance  of  such  discrep- 
ancies in  scientific  research,  and  he  called  them 
residual  phenomena. 

An  illustration  of  such  a  situation  and  the  solu- 
tion of  the  problem  thus  presented  is  that  of  Sir 
Humphry  Davy's  experiments  upon  the  decomposi- 
tion of  water  by  galvanism.  "He  found  that 
besides  the  two  components  of  water,  oxygen  and 
hydrogen,  an  acid  and  alkali  were  developed  at  the 
two  opposite  poles  of  the  machine.  As  the  theory 
of  the  analysis  of  water  did  not  give  reason  to  ex- 
pect these  products,  they  were  a  residual  x>henome- 
non,  the  cause  of  which  was  still  to  be  found.  The 
insight  of  Davy  conjectured  that  there  might  be 
some  hidden  cause  of  this  portion  of  the  effect ;  the 
glass  containing  the  water  might  suffer  partial 
decomposition,  or  some  foreign  matter  might  be 
mingled  with  the  water,  and  the  acid  and  alkali  be 
disengaged  from  it,  so  that  the  water  would  have 
no  share  in  their  production.      Assuming  this,  he 


150  INDUCTIVE  LOGIC 

proceeded  to  try  whether  the  total  removal  of  the 
cause  would  destroy  the  effect  produced.  By  the  sub- 
stitution of  gold  vessels  for  the  glass,  without  any 
change  in  the  effect,  he  at  once  determined  that  the 
glass  was  not  the  cause.  Employing  distilled  water, 
he  found  a  marked  diminution  of  the  quantity  of  acid 
and  alkali  evolved;  yet  there  was  enough  to  show 
that  the  cause,  whatever  it  was,  was  still  in  opera- 
tion. The  impurity  of  the  Avater,  then,  was  not  the 
sole,  but  a  concurrent  cause.  He  now  conceived 
that  the  perspiration  from  the  hands  touching  the 
instruments  might  affect  the  case,  as  it  would  con- 
tain common  salt,  and  an  acid  and  alkali  would 
result  from  its  decomposition  under  the  agency  of 
electricity.  By  carefully  avoiding  such  contact,  he 
reduced  the  quantit}^  of  the  products  still  further, 
until  no  more  than  slight  traces  of  them  were  per- 
ceptible. What  remained  of  the  effect  might  be 
traceable  to  impurities  of  the  atmosphere  decom- 
posed by  contact  with  the  electrical  apparatus. 
An  experiment  determined  this ;  the  machine  was 
placed  under  an  exhausted  receiver,  and  when  thus 
secured  from  atmospheric  influence,  it  no  longer 
evolved  the  acid  and  alkali."^ 

By  means  of  the  suggestions  incident  upon  this 
method,  Bunsen,  in  1860,  discovered  two  new  alka- 
line metals,  caesium  and  rubidium.  He  was  ex- 
amining alkalies  produced  by  the  evaporation  of 
mineral  water  from  Dlirkheim.  The  flame  of  these 
salts  was  examined  by  the  spectroscope.  Bunsen 
discovered  several  bright  lines  which  he  had  never 
1  Gore,  The  Art  of  Scientific  Discovery,  pp.  432, 433. 


THE  METHOD  OF  RESIDUES  151 

noticed  before,  and  which  he  knew  could  not  be 
produced  by  potash  or  soda,  whose  corresponding 
lines  were  in  close  proximity.  He  then  subjected 
the  mixture  to  a  searching  analysis  and  succeeded 
in  obtaining  two  new  alkaline  substances.  When 
he  had  separated  them,  he  then  tested  them  by  the 
method  of  difference,  by  which  he  found  that  they 
were  capable  of  producing  the  lines  at  first  noticed; 
but  when  withdrawn,  the  lines  instantaneously  dis- 
appeared. 

Thomson  and  Tait,  in  their  Elements  of  Natural 
Philosophy,  have  the  following  reference  and 
illustration  of  this  method.  "  When,  in  an  ex- 
periment, all  known  causes  being  allowed  for, 
there  remain  unexplained  effects  (excessively 
slight  it  may  be),  these  must  be  carefully  inves- 
tigated, and  every  conceivable  variation  of  ar- 
rangement of  apparatus,  etc.,  tried ;  until,  if 
possible,  we  manage  so  to  exaggerate  the  residual 
phenomenon  as  to  be  able  to  detect  its  cause.  It 
is  here,  perhaps,  that  in  the  present  state  of 
science  we  may  most  reasonably  look  for  exten- 
sions of  our  knowledge ;  at  all  events,  we  are 
warranted  by  the  recent  history  of  natural  phi- 
losophy in  so  doing.  Thus,  to  take  only  a  very 
few  instances,  and  to  say  nothing  of  the  discovery 
of  electricity  and  magnetism  by  the  ancients,  the 
peculiar  smell  observed  in  a  room  in  which  an 
electrical  machine  is  kept  in  action  was  long 
ago  observed,  but  called  the  '  smell  of  electricity,' 
and  thus  left  unexplained.  The  sagacity  of  Schon- 
bein  led  to  the  discovery  that  this  is  due  to  the 


152  INDUCTIVE  LOGIC 

formation  of  ozone,  a  most  extraordinary  body, 
of  enormous  chemical  energies ;  whose  nature  is 
still  uncertain,  though  the  attention  of  chemists 
has  for  years  been  directed  to  it."^ 

Another  illustration  of  this  method  is  seen  in 
the  comparison  of  the  observed  and  calculated 
positions  of  Encke's  comet.  It  was  found  that 
the  comet  returned  a  little  sooner  than  it  should 
have  done,  the  period  regularly  decreasing  from 
1212.79  days,  between  1786  and  1789,  to  1210.44 
between  1855  and  1858.  The  inference  has  been 
that  there  is  a  resisting  medium,  as  the  ether, 
filling  the  space  through  which  the  comet  passes. 
AVhat  the  resisting  medium  is,  and  its  nature,  is 
of  course  a  matter  of  conjecture  as  far  as  re- 
vealed by  this  method  alone.  The  method  merely 
indicates  some  resisting  medium  to  account  for 
the  observed  discrepancy.^ 

Herschel  has  observed  that  all  great  astronom- 
ical discoveries  have  been  disclosed  in  the  form 
of  residual  differences.  The  practice  was  intro- 
duced by  Halley,  when  astronomer  royal,  of 
comparing  systematically  the  positions  of  the 
heavenly  bodies  as  actually  observed  with  what 
might  have  been  expected  theoretically.  His  re- 
ductions of  the  lunar  observations  gave  a  series 
of  residual  errors,  extending  from  1722  to  1739. 
These  were  carefully  tabulated,  and  formed  the 
basis  for  certain  modifications  of  the  lunar  theory.^ 

1  Thomson  and  Tait,  Elements  of  Natural  Philosophy,  Vol.  I. 
pp. 113  f . 

2  Jevons,  Principles  of  Science,  p.  570.  ^  ihia.  p.  572. 


THE  METHOD  OF  RESIDUES  163 

A  discrepancy  was  observed  by  Newton  between 
the  theoretical  and  actual  velocity  of  sound;  the 
former  being  968  feet  per  second,  and  the  latter 
1142.  Newton's  experiments  and  calculation  were 
both  inaccurate;  nevertheless,  a  real  discrepancy 
has  been  proved  to  exist,  the  theoretical  being 
916  and  the  real  velocity  1090  feet  per  second. 
In  1816  La  Place  showed  this  difference  to  be 
due  to  the  heat  evolved  by  the  sudden  compres- 
sion of  the  air  during  the  propagation  of  the 
sound  wave,  the  heat  having  the  effect  of  in- 
creasing the  elasticity  of  the  air,  and  therefore 
appreciably  accelerating  the  sound  impulse. 

It  sometimes  happens  that  in  repeating  an  ex- 
periment, we  are  confronted  with  evidently  different 
results.  Then,  we  may  be  sure,  the  experiment  has 
been  carelessly  or  inaccurately  performed ;  or  else 
there  are  some  disturbing  causes  not  observed  by 
us.  On  the  other  hand,  however,  if  there  is  no 
likelihood  of  coincidence  on  repeated  trials,  yet, 
nevertheless,  a  marked  agreement  is  noticed  in  the 
results  of  various  trials,  the  mind  should  be  at 
once  alert  to  discover  the  hidden  cause  of  such 
agreement,  and  possibly  may  be  led  to  new  truths 
of  great  importance.  The  following  illustration  is 
given  by  Thomson  and  Tait :  "  With  a  very  good 
achromatic  telescope  a  star  appears  to  have  a  sensi- 
ble disc.  But,  as  it  is  observed  that  the  discs  of  all 
stars  appear  to  be  of  equal  angular  diameter,  we  of 
course  suspect  some  common  error.  Limiting  the 
aperture  of  the  object-glass  increases  the  appear- 
ance in  question,  which,  on  full  investigation,  is 


154  INDUCTIVE  LOGIC 

found  to  have  nothing  to  do  with  discs  at  all.  It 
is,  in  fact,  a  phenomenon  due  to  diffraction  of 
light."  ^ 

It  Avas  said  of  Darwin  that  in  his  researches  the 
residual  phenomena  were  always  the  special  objects 
of  his  attention.  His  son,  Francis  Darwin,  says  of 
him:  "There  was  one  quality  of  mind  which  seemed 
to  be  of  special  and  extreme  advantage  in  leading 
him  to  make  discoveries.  It  was  the  power  of 
never  letting  exceptions  pass  unnoticed.  Every- 
body notices  a  fact  as  an  exception  when  it  is  strik- 
ing or  frequent,  but  he  had  a  special  instinct  for 
arresting  an  exception.  A  point  apparently  slight 
and  unconnected  with  his  present  work  is  passed 
over  by  many  a  man  almost  unconsciously,  with 
some  half-considered  explanation,  which  is  in  fact 
no  explanation.  It  was  just  these  things  that  he 
seized  upon  to  make  a  start  from.  In  a  certain 
sense  there  is  nothing  special  in  this  procedure, 
many  discoveries  being  made  by  means  of  it.  I 
only  mention  it,  because,  as  I  watched  him  at  his 
work,  the  value  of  this  power  to  an  experimenter 
was  so  strongly  impressed  upon  me."  ^  This  is 
striking  testimony  as  to  the  practical  worth  of  this 
method  as  an  instrument  of  research. 

This  method  has  also  been  applied  to  the  more 
practical  usage  of  examining  the  refuse  of  manu- 
factured and  other  products  in  order  to  discover 

1  Thomson  and  Tait,  Elements  of  Natural  Philosophy,  Vol.  I. 
p.  114. 

2  F.  Darwin,  Life  and  Letters  of  Charles  Darwin,  Vol.  I. 
p.  125. 


THE  METHOD  OF  RESIDUES  155 

some  concealed  utility.  The  analysis  of  coal-tar 
refuse  has  led  to  the  discovery  of  many  valuable 
substances  that  have  proved  of  use  in  the  arts,  and 
in  medicine  as  well.  Glauber,  the  eminent  chemist, 
and  a  discoverer  of  several  chemical  compounds, 
said  he  made  it  a  rule  to  examine  what  every  other 
chemist  threw  away. 


CHAPTER  XII 

Verification  and   Prediction 

Tlie  Inclucto-deductive  Method.  —  We  have  seen 
that  the  inductive  methods  are  efficient  in  revealing 
the  cause  of  a  given  phenomenon  under  investiga- 
tion; and  yet  they  do  not  warrant  us  in  general- 
izing the  special  instance  so  as  to  formulate  a 
universal  law.  There  is  always  the  possibility 
that  while  the  special  case  which  we  experiment 
upon  may  give  us  indications  of  an  existing  causal 
relation,  still  a  wider  experience  might  disprove,  or 
else  modify  materially  our  conclusions.  The  well- 
recognized  fact  of  the  plurality  of  causes  and  the 
intermixture  of  effect  further  embarrasses  us  in 
the  attempt  to  rise  to  a  law  having  universal  sig- 
nificance and  validity.  The  results  of  the  induc- 
tive methods,  therefore,  need  to  be  supplemented 
by  some  corroborative  observations  or  experiments 
that  will  conclusively  verify  the  results  as  obtained. 
This  supplementary  method  is  one  Avhich  combines 
deduction  with  induction.  Mr.  Mill  calls  it  the 
Deductive  Method.  It  is,  however,  more  ade- 
quately designated  by  the  name,  the  Inducto-de- 
ductive  Method.     It  consists  of  three  stages  :  — 

1.  Obtaining,  by  the  inductive  methods  already 
150 


VERIFICATION   AND  PREDICTION  157 

described,  the  evidence  of  some  existing  causal 
connection,  tentatively  expressed  in  the  form  of  a 
universal  law. 

2.  Regarding  this  universal  law  as  the  basis  for 
subsequent  deductions,  by  which  we  gain  a  knowl- 
edge of  the  nature  of  unknown  phenomena,  as 
necessitated  by  the  conditions  of  this  law. 

3.  Verifying  the  results  thus  obtained  by  their 
correspondence  with  the  phenomena  as  actually 
observed.  Where  this  correspondence  is  wanting, 
then  either  the  law  was  not  correctly  expressed,  or 
there  must  have  been  some  error  in  our  deduction 
based  upon  it.  When  we  are  assured  that  the  lat- 
ter is  not  the  case,  then  a  discrepancy  between  the 
theoretically  deduced  result  and  the  actual  facts  as 
observed,  always  discredits  our  original  induction. 
This  method  of  verification  serves  as  a  check  upon 
hasty  generalization,  on  the  one  hand;  and  on  the 
other,  it  serves  to  extend  our  knowledge  into  un- 
known regions,  and  is  valuable  as  a  means  of  scien- 
tific prediction.  In  the  development  of  scientific 
knowledge,  it  has  been  a  potent  factor  in  enlarging 
the  bounds  of  knowledge  beyond  the  sphere  of  im- 
mediate observation. 

This  combined  process  of  reasoning  is  the  one 
commonly  employed  by  us  all.  Induction  and  de- 
duction are  not  separate  processes,  but,  as  before 
remarked,  they  are  complementary  factors  in  the 
one  actual  process  of  reasoning.  We  are  con- 
tinually using  our  inductions  as  a  deductive  basis, 
inferring  how  things  should  be  before  they  are 
really  seen;  and,  when  seen,  at  once  instinctively 


158  INDUCTIVE  LOGIC 

comparing  prior  inference  with  present  fact,  we 
are  either  confirmed  in  our  reasoning  process,  or 
compelled  to  discard  our  previous  inference  as 
false  or  inadequate  as  the  case  may  be.  Our 
world,  the  world  of  knowledge,  is  built  up  of  the 
seen,  and  the  unseen  as  well,  because  necessitated 
by  inferences  growing  out  of  the  seen  which  we  are 
constrained  to  make ;  the  unseen  which  we  thus 
are  continually  building  into  the  seen  and  regard- 
ing it  as  though  the  known,  we  are,  however, 
from  time  to  time  compelled  to  alter,  and  here  and 
there  tear  down  what  we  have  too  rashly  builded 
up,  as  the  structure  is  put  to  the  test  of  verifying 
fact. 

This  method  of  verification  was  used  to  decide 
between  inferences  drawn  by  Newton  and  Huy- 
ghens  respectively,  regarding  the  nature  of  light. 
Newton's  observations  led  him  to  infer  that  light 
consisted  of  particles  of  matter  shot  out  from  the 
sun.  Huyghens  insisted  that  light  consisted  in  the 
propagation  of  some  kind  of  disturbance  in  the  man- 
ner of  a  wave-motion.  Newton's  theory  being  taken 
as  established,  it  would  necessitate  that  light  on 
entering  a  denser  body  of  water,  being  refracted 
more  nearly  in  a  direction  perpendicular  to  the 
surface,  should,  accordingly,  move  faster  in  the 
denser  body  than  in  the  rarer  one  outside.  On 
the  other  hand,  according  to  Huyghens'  theory,  the 
opposite  effect  should  take  place,  —  light  being  re- 
fracted towards  the  vertical  at  the  horizontal  sur- 
face of  a  dense  body  such  as  water,  its  velocity  in 
the  dense  body  should  be  less  than  its  velocity  in 


VERIFICATION  AND  PREDICTION  159 

the  rare  body.  The  experiments  separately  made 
by  Fizeau  and  Foucault,  both  gave  the  result  that  in 
water  light  moves  slower  than  in  air,  and  therefore 
the  theory  of  Huyghens,  which  was  in  accord  with 
such  a  fact,  was  verified,  and  the  theory  of  Newton, 
which  was  radically  out  of  harmony  with  such  a 
fact,  was  discredited.^ 

We  cannot  theorize  concerning  nature  to  any  con- 
siderable extent  without  resorting  to  nature  again 
to  correct  aberrations  of  reason,  and  the  false 
fancies  of  the  imagination.  Theory,  if  correctly 
formulated,  will  always  lead  to  a  representation 
of  facts  as  they  are ;  just  as  facts  as  they  are,  if 
rightly  interpreted,  will  always  lead  to  correct 
theory. 

The  following  are  illustrations  of  the  value  of 
this  method  in  predicting  results  before  unknown. 

^'  Halley  had  the  glory  of  having  first  detected  a 
periodic  comet  in  the  case  of  that  which  has  since 
borne  his  name.  In  1705,  Halley  explained  how 
the  parabolic  orbit  of  a  planet  may  be  determined 
from  thr§e  observations;  and  joining  example  to 
precept,  himself  calculated  the  positions  and  orbits 
of  twenty-four  comets.  He  found,  as  the  reward 
of  his  industry,  that  the  comets  of  1607  and  1531 
had  the  same  orbit  as  that  of  1682.  And  here  the 
intervals  are  nearly  the  same,  namely,  about  seventy- 
five  years.  Are  these  three  comets  then  identical  ? 
In  looking  back  into  the  history  of  such  appear- 
ances, he  found  comets  recorded  in  1456,  in  1380, 
and  1305;  the  intervals  are  still  the  same,  —  sev- 

1  Tait,  Recent  Advances  in  Physical  Science,  pp.  65, 66. 


160  INDUCTIVE  LOGIC 

enty-five  or  seventy-six  years.  It  was  impossible 
now  to  doubt  that  they  were  the  periods  of  a  revolv- 
ing body,  its  orbit  a  long  ellipse,  not  a  parabola.  If 
this  were  so,  the  comet  must  reappear  in  1758  or 
1759.  Halley  began  his  laborious  calculations  and 
predicted  that  the  comet  would  reach  its  perihelion 
April  13,  1759,  but  claimed  the  license  of  a  month 
for  the  inevitable  inaccuracies  of  a  calculation  in 
which,  in  addition  to  all  other  sources  of  error,  was 
made  in  haste,  that  it  might  appear  as  a  prediction. 
The  comet  justified  his  calculations  and  his  caution 
together ;  for  it  arrived  at  its  perihelion  on  March 
13,  1759." ' 

Another  illustration  of  a  like  nature  is  the  pre- 
diction of  Faraday,  based  upon  Wheatstone's  ex- 
perimental proof  that  the  conduction  of  electricity 
required  time;  namely,  'Hhat  if  the  conducting 
wires  were  connected  Avith  the  coatings  of  a  large 
Leyden  jar,  the  rapidity  of  conduction  would  be 
necessarily  lessened.  This  prediction  was  made  in 
1838  and  was  not  verified  until,  sixteen  years  later, 
a  submarine  cable  was  laid  beneath  the  English 
Channel.  A  considerable  retardation  of  the  electric 
spark  was  then  detected  by  Siemens  and  Latimer 
Clark.  Faraday  at  once  pointed  out  that  the  wire 
surrounded  by  water  resembles  a  Leyden  jar  on  a 
large  scale :  so  that  each  message  sent  through  the 
cable  verified  his  remark  of  1838."  ^ 

In  Pasteur's  experiments  with  silkworms  already 
referred  to,  he   made  a  prediction  in  1866,  when, 

1  Whewell,  Hlstonj  of  Inductive  Science,  3d  ed.  Vol.  II.  p.  182, 

2  Jevons,  Principles  of  Science,  p.  543. 


VERIFICATION  AND  PREDICTION  161 

having  inspected  fourteen  parcels  of  eggs  intended 
for  incubation,  and  having  examined  the  moths 
which  produced  these  eggs,  he  wrote  out  the  pre- 
diction of  what  wouki  occur  in  18G7,  and  placed 
the  prophecy  as  a  sealed  letter  in  the  hands  of  the 
mayor  of  St.  Hippolyte.  In  1867,  the  cultivators 
communicated  to  the  mayor  their  results.  The 
letter  of  Pasteur  was  then  opened  and  read,  and  it 
was  found  that  in  twelve  out  of  fourteen  cases 
there  was  absolute  conformity  between  his  predic- 
tion and  the  observed  facts.  Many  of  the  groups 
had  perished  totally;  the  others  had  perished 
almost  totally ;  and  such  was  Pasteur's  prediction. 
In  two  out  of  the  fourteen  cases,  instead  of  the 
prophesied  destruction,  half  an  average  crop  was 
obtained.^ 

Another  interesting  illustration  concerns  Dar- 
win's speculations  regarding  the  formation  of  coral 
reefs  and  atolls.  Before  Darwin  wrote  on  the 
subject,  it  was  generally  believed  that  the  coral 
atolls  were  formed  by  the  coral  polypes  growing 
upon  submerged  volcanic  craters.  Darwin  insisted 
that  as  the  polypes  cannot  live  below  a  depth  of 
100  feet,  and  are  killed  by  exposure  to  sunshine  and 
air,  and  could  not  therefore  have  grown  upward 
from  the  vast  depths  to  which  the  coral  masses 
extend,  each  atoll  must  have  begun  as  a  fringing- 
reef  about  an  island  almost  tonching  the  shore,  Avith 
only  a  narrow  and  shallow  channel  of  water  be- 
tween ;  and  then  became  a  barrier  reef,  that  is,  one 
with  a  wider  and  deeper  channel  of  water  separat- 
i  TjndsiM,  Fragments  of  Science,  pp.  291,  292. 

M 


162  INDUCTIVE  LOGIC 

ing  from  the  shore,  owing  to  the  slow  but  progres- 
sive subsidence  of  the  island  round  which  the 
polypes  first  began  to  build.  Then  with  the  further 
and  complete  subsidence  of  the  island  beneath  the 
water,  there  remained  a  ring  of  coral  with  a  central 
lagoon  forming  the  so-called  atoll.  Darwin  says  in 
his  Autobiography  that  the  main  features  of  his 
theory  were  conceived  while  on  the  voyage,  and 
that  even  previous  to  seeing  a  true  coral  reef.^  He 
says :  "  No  other  work  of  mine  was  begun  in  so 
deductive  a  spirit  as  this,  for  the  whole  theory  was 
thought  out  on  the  west  coast  of  South  America, 
before  I  had  seen  a  true  coral  reef.  I  had  only  to 
verify  and  extend  my  views  by  a  careful  examina- 
tion of  living  reefs.  But  it  should  be  observed 
that  I  had  during  the  two  previous  years  been  in- 
cessantly attending  to  the  effects  on  the  shores  of 
South  America  of  the  intermittent  elevation  of  the 
land,  together  with  denudation  and  deposition  of  sedi- 
ment. This  necessarily  led  me  to  reflect  much  on  the 
effects  of  subsidence,  and  it  was  easy  to  replace  in 
imagination  the  continued  deposition  of  sediment 
by  the  upward  growth  of  corals.  To  do  this  was 
to  form  my  theory  of  the  formation  of  barrier  reefs 
and  atolls." 

It  will  thus  be  seen  that  Darwin's  deduction  was 
based  upon  previous  inductions  in  other  spheres, 
the  result  of  his  own  observation ;  he  also  tells  us 
in  the  same  connection,  that  he  had,  in  the  prepa- 
ration of  his  work  on  Coral  Reefs,  spent  twenty 
months  of  hard  labor,  reading  every  work  on  the 

1  Life  and  Letters  of  Charles  Darwin,  1887,  Vol.  I.  p.  58. 


VERIFICATION  AND  PREDICTION  163 

islands  of  the  Pacific  and  consulting  many  charts. 
He  thus  made  the  widely  extended  observations  of 
other  men  tributary  to  his  inferences  concerning 
coral-reef  formations.  Dr.  Williams  says  of  Dar- 
win's insight  in  this  particular:  "He  saw  more 
clearly  than  his  precursors  had  done  the  validity 
of  the  dictum  of  Johannes  Miiller  in  this,  and 
indeed  all  his  works,  that  the  most  important 
truths  in  natural  science  are  to  be  discovered, 
neither  by  the  mere  analysis  of  i3hilosophical  ideas, 
nor  by  simple  experience,  but  by  reflective  experience, 
which  distinguishes  the  essential  from  the  acciden- 
tal in  the  phenomena  observed,  and  thus  finds 
principles  from  which  many  experiences  can  be 
derived."^  This  is  a  very  satisfactory  and  strik- 
ing account  of  what  may  be  styled  the  combined 
inducto-deductive  temper  of  mind,  and  especially 
as  embodied  in  so  eminent  a  student  of  nature  as 
Darwin. 

Bacon  insists  that  anticipations  of  nature  are 
sources  of  innumerable  errors,  and  that  the  truly 
scientific  method  consists  in  an  interpretation  of 
nature  as  it  .is  revealed  to  the  perception  through 
direct  observation  and  experiment.  It  is,  however, 
largely  through  these  "  anticipations  "  that  progress 
in  science  is  attained.  There  may  be  anticipations 
which  are  considered  final,  and  all  attempts  at  veri- 
fication regarded  as  unnecessary  and  even  as  im- 
pertinent. Eesults  deductively  attained  are  then 
asserted  with  dogmatic  insistence,  as  though  pos- 

1  Darwin,  Coral  Reefs.  Prefatory  note  by  Dr.  J.  W.  Williams, 
p.  ix. 


164  INDUCTIVE  LOGIC 

sessing  the  convincing  power  of  facts  themselves; 
and  all  appeal  to  controverting  or  exceptional  cases 
are  set  aside,  without  even  so  much  as  a  respectful 
hearing.  Such  anticipations  of  nature  rightfully 
fall  under  the  scornful  reprehension  of  a  Bacon. 
But  there  are  other  anticipations  which  serve  as 
a  spur  to  a  more  penetrating  observation,  and  more 
painstaking  experiment,  in  order  to  square  theory  to 
facts.  Such  anticipations  are  the  glory  of  science ! 
Suppose  such  anticipations  are  disproved  by 
subsequent  experiment  or  observation ;  they  have 
served  a  high  purpose  in  suggesting  investigation 
along  lines  which  otherwise  would  have  remained 
unthought  of.  Anticipations  alone  are  barren ;  an- 
ticipations leading  to  verification  are  productive  of 
valuable  results.  To  this  the  history  of  scientific 
thought  bears  abundant  testimony.  Professor  Clif- 
ford has  made  the  power  of  prediction  one  of  the 
essential  characteristics  of  scientific  thought.  He 
says,  in  his  essay  on  the  Aims  and  Instruments  of 
Scientific  Thought,  that  "  the  difference  between  sci- 
entific and  merely  technical  thought  is  just  this  : 
Both  of  them  make  use  of  experience  to  direct  hu- 
man action;  but  while  technical  thought  or  skill 
enables  a  man  to  deal  with  the  same  circumstances 
that  he  has  met  with  before,  scientific  thought  en- 
ables him  to  deal  with  different  circumstances  that 
he  has  never  met  with  before."  ^  He  cites  two  illus- 
trations, which  are  admirable  examples  of  scientific 
prediction.  The  first  relates  to  the  suggestion  of 
rieeming  Jenkin,  regarding  structural  bracing.  It 
1  Clifford,  Lectia^es  and  Essays,  Vol.  I.  p.  128. 


VERIFICATION  AND  PREDICTION  165 

had  been  known  before  that  in  an  arch  every  part 
is  compressed  or  pushed  by  other  parts;  and  every 
part  of  a  chain  is  in  a  state  of  tension,  that  is, 
pulled  by  the  other  parts.  In  many  cases  these 
forms  are  united  in  the  common  girder,  which  con- 
sists of  two  main  |)ieces,  of  which  the  upper  acts 
as  an  arch,  and  is  compressed,  while  the  lower  one 
acts  as  a  chain  and  is  pulled.  "  Now,"  says  Profes- 
sor Clifford,  "  suppose  that  any  good,  practical  engi- 
neer makes  a  bridge  or  a  roof  upon  some  approved 
pattern  which  has  been  made  before.  He  designs 
the  size  and  shape  of  it  to  suit  the  opening  which 
has  to  be  spanned ;  selects  his  material  according 
to  the  locality  ;  assigns  the  strength  which  must  be 
given  to  the  several  parts  of  the  structure,  accord- 
ing to  the  load  which  it  will  have  to  bear.  There 
is  a  great  deal  of  thought  in  the  making  of  this 
design,  whose  success  is  predicted  by  the  applica- 
tion of  previous  experience  ;  it  requires  technical 
skill  of  a  vcLy  high  order,  but  it  is  not  scientific 
thought.  On  the  other  hand,  Mr.  Fleeming  Jenkin 
designs  a  roof  consisting  of  two  arches  braced  to- 
gether, instead  of  an  arch  and  a  chain  braced 
together ;  and,  although  this  form  is  quite  different 
from  any  known  structure,  yet  before  it  is  built  he 
assigns  with  accuracy  the  amount  of  material  that 
must  be  put  into  every  part  of  the  structure  in 
order  to  bear  the  required  load,  and  this  prediction 
may  be  trusted  with  perfect  security.  What  is  the 
natural  comment  on  this  ?  Why,  that  Mr.  Fleeming 
Jenkin  is  a  scientific  engineer."  ^ 

1  Clifford,  Lectures  and  Essays,  Vol.  I.  pp.  127, 128. 


166  INDUCTH^  LOGIC 

The  second  illustration  which  Professor  Clifford 
gives  is  as  follows :  '^  You  know  that  if  3'ou  make  a 
dot  on  a  piece  of  paper,  and  then  hold  a  piece  of 
Iceland  spar  over  it,  you  will  see  not  one  dot,  but 
two.  A  mineralogist,  by  measuring  the  angles  of  a 
crystal,  can  tell  you  whether  or  no  it  possesses  this 
property  without  looking  through  it.  He  requires 
no  scientific  thought  to  do  that.  But  Sir  William 
Eowan  Hamilton,  the  late  astronomer  royal  of  Ire- 
land, knowing  these  facts,  and  also  the  explanation 
of  them,  which  Fresnel  had  given,  thought  about  the 
subject,  and  he  predicted  that  by  looking  through 
certain  crystals  in  a  particular  direction  we  should 
see  not  two  dots,  but  a  continuous  circle.  Mr.  Lloyd 
made  the  experiment  and  saw  the  circle,  a  result 
w^hich  had  never  been  even  suspected.  This  has 
always  been  considered  one  of  the  most  signal 
instances  of  scientific  thought  in  the  domain  of 
physics.  It  is  most  distinctly  an  application  of 
experience  gained  under  certain  circumstances  to 
entirely  different  circumstances."  ^ 

There  is  also  an  indirect  method  of  prediction, 
varying  somewhat  from  the  one  already  described 
and  yet  similar  to  it.  It  is  called  prediction  by 
inversion  of  cause  and  effect.  There  are  many 
cases  in  which  cause  and  effect  are  related  in  a 
reciprocal  manner,  so  that  not  only  will  the  cause 
produce  the  effect,  but  the  effect,  operating  as  a 
cause,  will  bring  about  the  original  cause  as  an 
effect,  it  may  be  in  a  modified  form  but  clearly  recog- 
nizable as  such.     Professor  Tyndall  said  of  Faraday 

1  Clifford,  Lectures  and  Essaijs,  Vol.  I.  pp.  128,  129. 


VERIFICATION  AND  PREDICTION  167 

that  "  the  strong  tendency  of  his  mind  to  look  upon 
the  reciprocal  actions  of  natural  forces  gave  birth 
to  his  greatest  discoveries."  ^  For  instance,  Oersted 
had  proved  that  an  electric  current  will  produce 
magnetism,  and  Faraday,  taking  this  as  a  suggestion, 
inferred  that  magnetism  might  produce  an  electric 
current;  in  the  year  1831  he  devised  a  suitable 
experiment  of  introducing  a  bar-magnet  into  a  coil 
of  insulated  copper  wire,  and  then  withdrawing  the 
magnet  whilst  the  two  ends  of  the  wire  were  con- 
nected with  a  distant  galvanometer,  which  indicated 
the  presence  of  the  electric  current.  Thus,  his  in- 
ference received  substantial  verification.^ 

It  has,  moreover,  been  found  that  when  a  given 
cause  produces  a  certain  effect,  then  if  the  effect  be 
produced  in  some  other  manner,  the  process  will  tend 
to  produce  the  original  cause,  but  inverted  as  regards 
its  direction  or  nature.  For  instance,  it  is  known 
that  heat  will  expand  gases  ;  now,  if  a  gas  be  re- 
lieved of  the  pressure  of  the  vessel  enclosing  it,  it  will 
expand  by  virtue  of  its  own  elastic  power,  produc- 
ing, however,  cold  in  the  surrounding  atmosphere. 
So  also  heat  will  cause  a  bar  of  iron  to  expand. 
Dr.  Joule  proved  that  if  iron  were  expanded  by 
mechanical  force,  it  would  be  accompanied  by  cold. 
Inasmuch  as  india-rubber  is  related  to  heat  in  an 
opposite  manner  to  that  of  iron,  being  contracted 
by  heat  instead  of  expanded,  we  would,  according 
to  the  law  above  expressed,  naturally  expect  that 
a  mechanical  expansion  of  india-rubber  would  give 

1  Tyndall,  Fragments  of  Science,  p.  338. 

2  Gore,  The  Art  of  Scientific  Discovei-y,  p.  594. 


168  INDUCTIVE  LOGIC 

heat,  and  a  contraction  produce  cold.  An  experi- 
ment may  be  tried  by  suddenly  stretching  a  rubber 
band  while  the  middle  part  is  in  the  mouth ;  when 
stretched,  it  grows  warm ;  when  relaxed,  it  seems 
cold.i 

Again,  as  heat  will  melt  many  substances,  if  we 
can  reduce  the  same  substance  from  the  solid  to 
the  liquid  -state,  we  would  expect,  as  a  result,  the 
negative  of  heat,  namely,  cold.  This  occurs  in  all 
freezing  mixtures,  as  the  affinity  of  salt  for  water 
causes  it  to  melt  ice,  thus  producing  cold  in  the 
surrounding  atmosphere,  sufficient  to  freeze  cream 
or  other  similar  substance,  inasmuch  as,  passing 
from  solid  to  liquid,  water  absorbs  heat  from  all 
substances  near  it ;  this  absorption  producing  arti- 
ficial cold  surrounding  it.  The  reciprocal  action 
of  heat  and  cold  is  illustrated  in  an  interesting  ex- 
periment described  by  Tait.^  He  took  a  bar  of  ice, 
supported  horizontally  at  either  end,  and  over  the 
middle  of  the  bar  he  put  a  fine  Avire,  and  put  equal 
weights  to  the  two  ends  of  the  wire.  The  wire 
gradually,  by  the  action  of  the  weights,  cut  through 
the  bar  of  ice,  and  yet  it  was  observed  that  the  path 
of  the  wire  was  instantly  replaced  by  the  freezing 
again  of  the  melted  portion  produced  by  the  press- 
ure, and  when  the  wire  had  wholly  traversed  the 
entire  thickness  of  the  bar,  the  bar  itself  was  intact, 
and  even  stronger  along  the  line  of  the  cutting  than 
before.  The  explanation  of  this  experiment  is  that 
inasmuch  as  heat  melts  ice,  then  when  ice  is  melted 

1  Jevons,  Principles  of  Science,  p.  545. 

■2  Tait,  Recent  Advances  in  Physical  Science,  pp.  99, 100. 


VERIFICATION  AND  PREDICTION  169 

by  pressure,  as  in  this  case  of  the  weighted  wire, 
cold,  the  negative  of  lieat,  is  induced ;  thus,  as  the 
wire  was  forced  by  the  weights  into  the  ice,  the  press- 
ure upon  the  ice  melted  it,  making  it  colder,  so  that 
the  water  produced,  passing  around  the  chilled  wire, 
and  being  thus  relieved  of  pressure,  froze  again. 

Faraday  predicted  certain  magnetic  phenomena 
by  this  method,  which  are  specially  interesting 
as  illustrations  of  this  kind  of  prediction.  It 
seems  that  Arago  had  observed  in  1824  that  the 
number  of  oscillations  which  a  magnetized  needle 
makes  in  a  given  time,  under  the  influence  of 
the  earth's  magnetism,  is  very  much  lessened  by 
the  proximity  of  certain  metallic  masses,  and  es- 
pecially of  copper.  Employing  the  latter  substance 
in  an  experiment  upon  a  magnetized  needle,  he  suc- 
ceeded in  reducing  the  number  of  its  vibrations  in 
a  given  time  from  three  hundred  to  four.  Taking 
the  experiment  as  a  basis  for  his  inference,  Fara- 
day predicted  that  since  the  presence  of  a  metal  at 
rest  stops  the  oscillations  of  a  magnetic  needle,  the 
neighborhood  of  a  magnet  at  rest  ought  to  stop 
the  motion  of  a  rotating  mass  of  metal.  He  there- 
fore proceeded  to  put  his  inference  to  the  test  of 
actual  experiment,  by  suspending  a  cube  of  copper 
to  a  twisted  thread  which  was  placed  between  the 
poles  of  a  powerful  electromagnet.  When  the 
thread  was  left  to  itself,  it  began  to  spin  round 
with  great  velocity,  but  stopped  the  moment  a 
powerful  current  passed  through  the  electromag- 
net.^    Again,  as  heat  applied   to   the   junction   of 

1  Ganot,  Phijslcs,  pp.  797,  798. 


170  INDUCTIVE  LOGIC 

two  metallic  bars,  as  antimony  and  bismuth,  pro- 
duced an  electric  current,  it  was  inferred  that  if  an 
electric  current  was  made  to  pass  through  such  a 
junction,  it  would  produce  cold,  and  such  proved  to 
be  the  case.^ 

In  the  general  process  of  verification,  it  often 
happens  that  seeming  exceptions  occur  which  are 
direct  contradictions  of  the  law  we  are  attempting 
to  prove.  And  it  is  in  dealing  with  such  cases 
that  one's  power  of  discrimination  is  most  fully 
taxed.  It  is  necessary  to  make  a  most  careful 
distinction  between  seeming  and  real  exceptions. 
Professor  Jevons  has  given  a  very  exhaustive  clas- 
sification of  the  different  kinds  of  exceptional 
phenomena,  which  it  is  well  to  have  in  mind,  in 
order  to  know  in  any  investigation  the  various  pos- 
sible complications  that  may  rise.^  The  excep- 
tional phenomena,  as  given  by  Jevons,  are  :  — 

1.  Imaginary,  or  false  exceptions ;  that  is,  facts, 
objects,  or  events  which  are  not  really  what  they 
are  supposed  to  be. 

2.  Apx^arent  but  congruent  exceptions,  which, 
though  apparently  in  conflict  with  a  law  of  nature, 
are  really  in  agreement  with  it. 

3.  Singular  exceptions,  which  really  agree  with 
a  law  of  nature,  but  exhibit  remarkable  and  unique 
results  of  it. 

4.  Divergent  exceptions,  which  really  proceed 
from   the  ordinary  action  of  known  processes  of 

1  Jevons,  Principles  of  Science,  p.  547. 

2  See  Jevons,  Chapter  XXIX.,  in  his  Principles  of  Science,  on 
"  Exceptional  Phenomena." 


VERIFICATION  AND  PREDICTION  171 

nature,   but   which    are    excessive   in    amount   or 
monstrous  in  character. 

5.  Accidental  exceptions,  arising  from  the  inter- 
ference of  some  entirely  distinct  but  known  law  of 
nature. 

6.  Novel  and  unexplained  exceptions,  which  lead 
to  the  discovery  of  a  new  series  of  laws  and  phe- 
nomena, modifying  or  disguising  the  effects  of  pre- 
viously known  laws  without  being  inconsistent 
with  them. 

7.  Limiting  exceptions,  showing  the  falsity  of 
a  supposed  law  to  some  cases  to  which  it  had  been 
extended,  but  not  affecting  its  truth  in  other  cases. 

8.  Contradictory,  or  real,  exceptions,  which  lead 
us  to  the  conclusion  that  a  supposed  hypothesis  or 
theory  is  in  opposition  to  the  phenomena  of  nature, 
and  must  therefore  be  abandoned. 

It  will  be  seen  that  among  so  many  possibilities 
of  interpretation  an  exception  does  not  necessarily 
prove  the  rule,  as  the  old  adage  would  have  it; 
nor  does  the  exception,  on  the  other  hand,  neces- 
sarily disprove  the  rule  or  law.  It  must  be  in  each 
case  strictly  and  adequately  interpreted,  Avhich  re- 
quires a  penetrating  sagacity  and  a  thorough  knowl- 
edge of  the  phenomena  under  investigation. 

In  the  process  of  verification,  the  question  nat- 
urally suggests  itself:  How  many  verifying  in- 
stances are  sufficient  to  determine  the  universal 
validity  of  a  given  law?  This  question  will  be 
recognized  as  an  old  difficulty,  now  presented  in 
another  form;  but  in  reality  it  is  the  perplexing 
problem  of  determining  the  logical  ground  of  in- 


172  INDUCTIVE   LOGIC 

duction.  What  is  our  warrant  for  proceeding  from 
known  and  verified  instances  to  unknown  phenom- 
ena, of  the  same  kind  it  is  true,  but  as  yet  beyond 
the  pale  of  our  experience  ?  The  warrant  for  our 
generalization  does  not  lie  wholly  in  the  number  of 
verifying  instances.  In  addition  to  the  effect  which 
mere  number  produces  in  confirming  our  belief, 
there  is  the  confidence  which  we  feel  in  the  con- 
stancy of  the  order  of  nature,  and  which  we  are 
constrained  to  assume  as  a  fundamental  postulate.^ 
Therefore,  we  say  that  the  verifying  facts  must  be 
of  such  a  number,  and  of  such  a  nature  as  well, 
that  they  give  evidence  of  a  uniformity  which 
transcends  all  supposition  of  mere  coincidence,  and 
compels  us  to  attribute  it  to  the  uniformity  of 
nature  itself,  in  which  we  find  a  warrant  for  our 
generalization.  As  Professor  Clifford  has  remarked : 
"  The  aim  of  scientific  thought  is  to  apply  past  ex- 
periences to  new  circumstances.  The  instrument 
is  an  observed  uniformity  in  the  course  of  events. 
By  the  use  of  this  instrument  it  gives  us  informa- 
tion transcending  our  experience,  it  enables  us  to 
infer  things  that  we  have  not  seen  from  things 
that  we  have  seen ;  and  the  evidence  for  the  truth 
of  that  information  depends  on  our  supposing  that 
the  uniformity  holds  good  beyond  our  experience."  ^ 
In  extending  knowledge  and  predicting  results 
beyond  the  sphere  of  experience,  modern  scientific 
investigation  is  largely  indebted  to  the  priuciples 
and  methods  of  mathematics.     Mathematical  laws, 

1  See  Siijwart,  Lor/ic,  Vol.  II.  p.  aiS. 

2  Clifford,  Lectures  and  Essays,  Vol.  I.  pp.  131,  132. 


VERIFICATION  AND  PREDICTION  173 

applied  to  the  data  given  in  sense-perception,  give 
indications  of  the  necessary  relations  that  must 
exist  in  the  observed  phenomena,  and  all  that  they 
involve.  Thus,  that  which  is  given  directly  in  con- 
sciousness is  supplemented  by  that  which  is  given 
indirectly  as  mathematically  necessitated.  The 
mathematico-experimental  method  in  physics  has 
led  to  very  rich  and  important  results  which  have 
proved  practically  its  efficiency  as  a  scientific 
method. 


CHAPTER   XIII 

Hypothesis 

The  inductive  process  cannot  proceed  to  any 
great  extent  or  attain  satisfactory  results  without 
the  aid  of  some  hypothesis.  An  hypothesis  is  a 
supposition  regarding  the  cause  of  a  phenomenon, 
which  we  make  either  as  preliminary  to  an  experi- 
ment which  will  prove  or  disprove  the  supposition, 
or  in  lieu  of  an  experiment  or  systematic  observa- 
tion when  such  are  impossible,  owing  to  the  peculiar 
conditions  of  the  phenomenon  itself.  We  see,  there- 
fore, that  the  framing  of  hypotheses  has  a  double 
function.  First,  considered  as  preliminary  to  ex- 
periment. We  found  that  in  cases  where  two,  three, 
or  more  elements  enter  into  a  complex  antecedent,  it 
is  impossible  often,  and  always  impracticable  to  test 
the  various  possible  combinations  separately  in  order 
to  note  their  different  results.  The  combinations  in 
complex  phenomena  are  indefinitely  great,  and  the 
isolation  of  certain  elements  in  order  to  estimate 
the  exact  result  of  the  combined  force  of  the  other 
combinations  is  extremely  difficult  and  often  im- 
possible. Therefore  the  mind  discards  some  com- 
binations as  irrelevant,  others  as  impossible,  and 
selects  one  perhaps  as  the  most  likely  cause  of  the 
174 


HYPOTHESIS  175 

given  effect.  This  selective  function  of  the  mind, 
therefore,  indicates  the  line  of  experiment  in  a  de- 
terminate manner  and  does  not  leave  the  phenom- 
ena to  indeterminate  and  haphazard  investigation. 
Consider,  for  instance,  so  eminent  an  experimenter 
as  Charles  Darwin,  so  fertile  in  all  kinds  of  experi- 
mental resources ;  yet  it  is  said  of  him  that  every 
experiment  was  the  result  of  a  tentative  theory, 
thought  out  in  advance  of  all  actual  test  by  a  saga- 
cious insight  into  the  necessary  conditions  of  the 
interrelated  phenomena  before  him.  His  son,  Fran- 
cis Darwin,  says  of  him  in  his  Remmiscences :  "  He 
often  said  that  no  one  could  be  a  good  observer 
unless  he  Avas  an  active  theorizer.  It  was  as  though 
he  were  charged  with  theorizing  power  ready  to 
flow  into  any  channel  on  the  slightest  disturbance, 
so  that  no  fact,  however  small,  could  avoid  releasing 
a  stream  of  theory,  and  thus  the  fact  became  mag- 
nified into  importance.  In  this  way,  it  naturally 
happened  that  many  untenable  theories  occurred  to 
him;  but  fortunately  his  richness  of  imagination 
was  equalled  by  his  power  of  judging  and  condemn- 
ing the  thoughts  that  occurred  to  him.  He  was 
just  to  his  theories,  and  did  not  condemn  them  un- 
heard ;  and  so  it  happened  that  he  was  willing  to 
test  what  would  seem  to  most  people  not  at  all 
worth  testing.  These  rather  wild  trials  he  called 
'  fool's  experiments,'  and  enjoyed  extremely.  As  an 
example,  I  may  mention  that,  finding  the  cotyledons 
of  Biophytum  to  be  highly  sensitive  to  vibrations 
of  the  table,  he  fancied  that  they  might  perceive 
the  vibrations  of  sound;  and  therefore  made  me  play 


176  INDUCTIVE   LOGIC 

my  bassoon  close  to  a  plant.  The  love  of  experiment 
was  very  strong  in  him,  and  I  can  remember  the  way 
he  would  say,  '  I  shan't  be  easy  till  I  have  tried  it,' 
as  if  an  outside  force  were  driving  him."  ^ 

Hypothesis  and  experiment  were  in  the  hand  of 
Darwin  like  a  two-edged  sword,  which  he  employed 
with  rare  skill  and  effect.  An  hypothesis  is  to  be 
regarded  not  only  as  the  precursor  of  experiment, 
but  it  also  functions  as  a  method  of  explanation 
when  actual  verification  is  impossible.  We  see 
this  constantly  in  our  every-day  life.  We  are  com- 
pelled again  and  again  to  account  for  situations 
which  occur  that  are  impossible  for  us  to  reproduce 
in  the  form  of  an  experiment,  that  we  are  able  to 
observe  but  once.  Some  explanation  is  required  to 
satisfy  mental  demands  which  are  imperative  in 
this  regard.  The  explanation  which  seems  most  in 
keeping  with  the  sum  of  facts  in  our  possession,  is 
the  hypothesis  which  we  frame ;  so  also  in  explain- 
ing the  conduct  of  others  by  conjecture  as  to  the 
most  reasonable  motives  that  will  satisfactorily 
account  for  the  same ;  such  hypotheses  we  are  con- 
stantly compelled  to  assume.  We  are  not  always 
able  to  perceive  the  relations  existing  between 
facts  as  they  come  into  the  sphere  of  our  experi- 
ence, and  yet  we  are  constrained  to  think  of  them 
as  related;  but  in  order  to  systematize  them,  we 
must  supply  mentally  the  lacunae  which  appear  in 
the  phenomena  as  perceived.  This  supposition  that 
is  necessary  to  construct  facts  into  system  is  an 
hypothesis. 

1  Life  and  Letters  of  Charles  Darwin,  Vol.  I.  p.  126. 


HYPOTHESIS  177 

An  illustration  of  an  hypothesis  suggesting  syste- 
matic observation  and  experiment  is  found  in  the 
history  of  the  discovery  of  vaccination  by  Jenner. 
It  seems  that  while  a  mere  youth,  pursuing  his 
studies  at  Sodbury,  he  chanced  to  hear  a  casual 
remark  made  by  a  country  girl  who  came  to  his 
master's  shop  for  advice.  The  small-pox  Avas  men- 
tioned, when  the  girl  said,  "  I  cannot  take  that  dis- 
ease, for  I  have  had  cow-pox."  ^  This  observation, 
expressing  the  common  superstition  of  the  simple 
country  folk,  appealed  to  Jenner's  mind  as  an  in- 
choate hypothesis.  Seizing  upon  it  as  a  suggestion 
of  possible  value,  he  proceeded  to  make  diligent 
inquiries  and  careful  observations,  which  finally 
led  him  to  the  discovery  of  vaccination. 

An  illustration  of  hypothesis  as  explanation  of 
phenomena  beyond  the  range  of  experiment  is  found 
in  the  hypothesis  as  to  the  source  of  the  sun's 
energy.  An  enumeration  of  the  different  hypothe- 
ses advanced  upon  this  subject  is  given  by  Tait  in 
his  Recent  Advances  in  Physical  Science?  "The 
old  notion  that  the  sun  is  a  huge  fire,  or  something 
of  that  kind,  is  one  which  will  only  occur  to  one 
thinking  of  the  matter  for  the  first  time  ;  but  with 
our  modern  chemical  knowledge,  we  are  enabled  to 
say  that,  massive  as  the  sun  is,  if  its  materials  had 
consisted  of  the  very  best  materials  for  giving  out 
heat,  that  enormous  mass  of  some  400,000  miles 
in  radius  could  have  supplied  us  with  only  about 
5000  years  of  the  present   radiation.     A   mass   of 

1  Gore,  The  Art  of  Scientific  Discovery,  p.  495. 

2  pp.  151  ff . 

N 


178  INDUCTIVE  LOGIC 

coal  of  that  size  would  have  produced  very  much 
less  than  that  amount  of  heat.  Nor  would  the 
most  energetic  chemicals  known  to  us,  combined 
in  proportion  for  giving  the  greatest  amount  of 
heat  by  actual  chemical  combination,  supply  the 
sun's  present  waste  for  even  5000  years.  There- 
fore as  we  all  know  that  geological  facts,  if  there 
were  no  others,  point  to  at  least  as  high  a  radiation 
from  the  sun  as  the  present,  for  at  all  events  a  few 
hundreds  of  thousands  of  years  back,  —  and  per- 
haps also  indicate  even  a  higher  rate  of  radiation 
from  the  sun  in  old  time  than  at  present,  —  it  is 
quite  obvious  that  the  heat  of  the  sun  cannot 
possibly  be  supplied  by  any  chemical  process  of 
which  we  have  the  slightest  conception. 

"Now,  if  we  can  find,  on  the  other  hand,  any 
physical  explanation  of  this  consistent  with  any 
present  knoAvledge,  we  are  bound  to  take  it  and  use 
it  as  far  as  we  can,  rather  than  say :  This  question 
is  totally  unanswerable  unless  there  be  chemical 
agencies  at  work  in  the  sun  of  a  far  more  power- 
ful order  than  anything  we  meet  with  on  the 
earth's  surface.  If  we  can  find  a  thoroughly  in- 
telligible source  of  heat,  which,  though  depending 
upon  a  different  physical  cause  from  the  usual 
one,  combustion,  is  amply  sufficient  to  have  sup- 
plied the  sun  with  such  an  amount  of  heat  as  to 
enable  it  to  radiate  for  perhaps  the  last  hundred 
millions  of  years  at  the  same  rate  as  it  is  now 
radiating,  then  I  say  we  are  bound  to  try  that 
hypothesis  first,  and  argue  upon  it  until  we  find  it 
inconsistent  with  something  known.     And   if   we 


HYPOTHESIS  179 

do  not  find  it  inconsistent  with  anything  that  is 
known,  while  we  find  it  completely  capable  of 
explaining  our  difficulty,  then  it  is  not  only  philo- 
sophic to  say  that  it  is  most  probably  the  origin 
of  the  sun's  energy,  but  we  feel  ourselves  con- 
strained to  admit  it.  Newton  long  ago  told  us 
this  obligation  in  his  Rules  of  Philosophizing. 
Now  it  is  known  that  if  we  were  to  take  a  mass 
of  the  most  perfect  combustibles  which  we  know, 
and  let  it  fall  upon  the  sun  merely  from  the 
earth's  distance,  then  the  work  done  upon  it  by 
the  sun's  attraction  during  its  fall  would  give  it  so 
large  an  amount  of  kinetic  energy  when  it  reached 
the  sun's  surface  as  to  produce  an  impact  which 
would  represent  six  thousand  times  the  amount  of 
energy  which  could  be  produced  by  its  mere  burn- 
ing. 

"It  appears,  then,  that  our  natural  and  only 
trustworthy  mode  of  explaining  the  sun's  heat  at 
present,  in  time  past,  and  for  time  to  come  must  be 
something  closely  analogous  to,  but  not  identical 
with,  what  was  called  the  nebular  hypothesis  of 
Laplace,  —  the  hypothesis  of  the  falling  together 
(from  rudely  scattered  distribution  in  space)  of 
the  matter  which  now  forms  the  various  suns  and 
planets.  We  find  by  calculation  in  which  there  is 
no  possibility  of  large  error,  that  this  hypothesis 
is  thoroughly  competent  to  explain  one  hundred 
millions  of  years'  solar  radiation  at  the  present 
rate,  perhaps  more ;  and  it  is  capable  of  showing 
us  how  it  is  that  the  sun,  for  thousands  of  years 
together^  can  part  with  energy   at  the   enormous 


180  INDUCTIVE  LOGIC 

rate  at  which  it  does  still  part  with  it,  and  yet 
not  apparently  cool  by  perhaps  any  measurable 
quantity. 

^^In  confirmation  of  this,  not  only  is  the  hy- 
pothesis itself  capable  of  explaining  the  amounts 
of  energy  which  are  in  question,  but  also  recent  in- 
vestigations, aided  by  the  spectroscope,  have  shown 
us  that  there  are  gigantic  nebular  systems  at  great 
distances  from  our  solar  system,  in  the  process  of 
physical  degradation  in  that  very  way,  by  the 
falling  together  of  scattered  masses,  and  with 
numerous  consequent  developments  of  heat  by 
impacts.  What  are  called  temporary  stars  form 
another  splendid  and  still  more  striking  instance 
of  it,  as  Avhere  a  star  suddenly  appears,  of  the  first 
magnitude,  or  even  brighter  than  the  first,  out- 
shining all  the  planets  for  a  month  or  two  at  a 
time,  and  then,  after  a  little  time,  becomes  invisi- 
ble in  the  most  powerful  telescope.  Things  of 
that  kind  are  constantly  occurring  on  a  larger  or 
smaller  scale  and  they  can  all  be  easily  explained 
on  this  supposition  of  the  impact  of  gravitating 
masses." 

Such  a  hypothesis,  it  will  be  seen,  embraces  all 
the  facts  observed  in  one  self-consistent  system. 
The  other  hypotheses  are  inadequate  to  account 
satisfactorily  for  the  phenomena.  The  validity 
of  this  hypothesis  lies  in  its  being  both  adequate 
and  congruent  as  well;  experiment  or  corroborative 
observation  being  out  of  the  question,  we  are,  as 
Tait  says,  "  constrained  to  admit  it." 

Mr.  Darwin  gives  an  enumeration  and  criticism 


HYPOTHESIS  181 

of  tlie  different  hypotheses  which  have  been  sug- 
gested to  explain  the  extinction  of  the  gigantic 
animals  known  to  have  existed  upon  the  earth. 
His  account  will  give  an  indication  of  the  natural 
propensity  of  the  mind  to  frame  hypotheses  con- 
cerning phenomena  which  lie  outside  the  sphere 
both  of  observation  and  experiment.  Mr.  Darwin 
says:  "It  is  impossible  to  reflect  on  the  changed 
state  of  the  American  Continent  without  the  deep- 
est astonishment.  Formerly  it  must  have  swarmed 
with  great  monsters;  now  we  find  mere  pigmies 
compared  with  the  antecedent  allied  races.  The 
greater  number,  if  not  all,  of  these  extinct  quad- 
rupeds, lived  at  a  late  period,  and  were  the  con- 
temporaries of  most  of  the  existing  sea-shells. 
What  then  has  exterminated  so  many  species  and 
whole  genera?  The  mind  at  first  is  irresistibly 
hurried  into  the  belief  of  some  great  catastrophe  ; 
but  thus  to  destroy  animals,  both  large  and  small, 
in  Southern  Patagonia,  in  Brazil,  on  the  Cordillera 
of  Peru,  in  North  America  up  to  Behring's  Straits, 
we  must  shake  the  entire  framework  of  the  globe. 

"An  examination,  moreover,  of  the  geology  of 
La  Plata  and  Patagonia  leads  to  the  belief  that 
all  the  features  of  the  land  result  from  slow  and 
gradual  changes.  It  appears  from  the  character 
of  the  fossils  in  Europe,  Asia,  Australia,  and  in 
North  and  South  America,  that  those  conditions 
which  favor  the  life  of  the  larger  quadrupeds 
were  lately  coextensive  with  the  world.  What 
those  conditions  were,  no  one  has  yet  even  con- 
jectured.    It  could  hardly  have  been  a  cliange  of 


182  INDUCTIVE  LOGIC 

temperature,  which  at  about  the  same  time  de- 
stroyed the  inhabitants  of  tropical,  temperate,  and 
arctic  latitudes  on  both  sides  of  the  globe.  In 
North  America  we  positively  know  from  Mr.  Lyell 
that  the  large  quadrupeds  lived  subsequently  to 
that  period  when  boulders  were  brought  into  lati- 
tudes at  which  icebergs  now  never  arrive;  from 
conclusive  but  indirect  reasons  we  may  feel  sure 
that  in  the  southern  hemisphere  the  Macrauchenia 
also  lived  long  subsequently  to  the  ice-transporting 
boulder-period.  Did  man,  after  his  first  inroad 
into  South  America,  destroy,  as  has  been  suggested, 
the  unwieldy  Megatherium  and  the  other  Eden- 
tata ?  We  must  look  at  least  to  some  other  cause 
for  the  destruction  of  the  little  tucutuco  at  Bahia 
Blanca,  and  of  the  many  fossil  mice  and  other 
small  quadrupeds  in  Brazil.  No  one  will  imagine 
that  a  drought,  even  far  severer  than  those  which 
cause  such  losses  in  the  provinces  of  La  Plata, 
could  destroy  every  individual  of  every  species 
from  Southern  Patagonia  to  Behring's  Straits. 
What  shall  we  say  of  the  extinction  of  the  horse  ? 
Did  those  plains  fail  of  pasture  which  have  since 
been  overrun  by  thousands  and  hundreds  of  thou- 
sands of  the  descendants  of  the  stock  introduced 
by  the  Spaniards  ?  Have  the  subsequently  intro- 
duced species  consumed  the  food  of  the  great 
antecedent  races  ?  Can  we  believe  that  the  Capy- 
bara  has  taken  the  food  of  the  Toxodon,  the 
Guanaco  of  the  Macrauchenia,  the  existing  small 
Edentata  of  their  numerous  gigantic  prototypes  ? 
Certainly  no  fact  in  tlie  long  history  of  the  world 


HYPOTHESIS  183 

is  so  startling  as  the  wide  and  repeated  exter- 
minations of  its  inhabitants."  ^  Mr.  Darwin's  own 
hypothesis  concerning  this  phenomenon  is  rather 
indefinite,  but  nevertheless  as  definite  as  the  ex- 
treme complexity  of  the  facts  will  allow.  He 
says  that  there  are  certain  causes  operating  in 
nature,  their  exact  character  remaining  unknown, 
such  that  the  too  rapid  increase  of  every  species, 
even  the  most  favored,  is  steadily  checked,  pro- 
ducing in  some  cases  rarity  and  in  others  ex- 
tinction, if  these  causes  operate  with  unusual 
efficacy.  His  hypothesis  marks  a  tendency  whose 
nature,  nevertheless,  remains  concealed. 

In  all  these  widely  differing  hypotheses  we  see  a 
certain  mental  constraint  to  offer  some  explanation, 
even  though  it  be  but  a  disguised  confession  of 
ignorance,  as  in  Mr.  Darwin's  hypothesis. 

An  illustration  of  an  hypothesis  to  explain  ob- 
served phenomena  that  cannot  be  further  tested  is 
that  given  in  the  following  instance  cited  by  Pro- 
fessor Tyndall :  "  At  Erith,  in  1864,  there  occurred 
a  tremendous  explosion  of  a  powder  magazine.  The 
village  of  Erith  was  some  miles  distant  from  the 
magazine,  but  in  nearly  all  cases  the  windows  were 
shattered ;  and  it  was  noticeable  that  the  windows 
turned  away  from  the  origin  of  the  explosion  suf- 
fered almost  as  much  as  those  which  faced  it.  Lead 
sashes  were  employed  in  Erith  church ;  and  these, 
being  in  some  degree  flexible,  enabled  the  windows 
to  yield  to  pressure  without  much  fracture  of  glass. 
Every  window  in  the  church,  front  and  back,  was 
1  DarwiD,  Voyage  of  a  Naturalist,  Vol.  I.  p.  223. 


184  INDUCTIVE  LOGIC 

bent  imcards.  In  fact,  as  the  sound-wave  reached 
the  church,  it  separated  right  and  left,  and,  for  a 
moment,  the  edifice  was  clasped  by  a  girdle  of  in- 
tensely compressed  air,  which  forced  all  its  win- 
dows inwards.  After  compression,  the  air  in  the 
church  no  doubt  dilated,  and  tended  to  restore  the 
windows  to  their  first  condition.  The  bending  in 
of  the  windows,  however,  produced  but  a  small 
condensation  of  the  whole  mass  of  air  within  the 
church;  the  force  of  the  recoil  was,  therefore, 
feeble  in  comparison  with  the  force  of  impact, 
and  insufficient  to  undo  what  the  latter  had  ac- 
complished." ^  Here  also  is  a  set  of  conditions 
that  must  be  satisfied  by  a  correct  hypothesis. 
The  phenomenon  was  not  capable  of  repetition  by 
any  experiment.  Professor  Tyndall,  therefore,  x^ict- 
ures  to  his  mind  what  must  have  happened  beyond 
that  which  was  observed,  in  order  to  account  for 
the  result  which  actually  happened.  He  fills  up 
the  unseen  from  what  he  knows  of  the  nature  of 
sound-waves,  and  thus  constructs  one  self-consistent 
system  which  includes  both  the  seen  and  the  un- 
seen, the  known  and  the  unknown,  the  observed 
and  the  inferred. 

It  will  be  noticed  in  this  and  other  illustrations 
of  hypothesis,  how  large  a  part  is  played  by  the 
imagination.  It  is  the  imagination  which  fills  out 
the  vacant  spaces  in  the  picture  of  perception. 
With  some,  the  function  of  imagination  is  asso- 
ciated with  fancy  rather  than  fact.  It  must,  in 
this   connection,   however,   be   clearly   emphasized 

1  Tyndall,  On  Sound,  p.  23. 


HYPOTHESIS  185 

that  the  imagination  which  constructs  hypotheses 
must  be  throughout  in  touch  with  fact.  It  must 
represent  to  the  mind,  not  what  fancy  suggests,  but 
what  the  known  facts  necessitate.  The  unseen  is 
constructed  out  of  the  determining  conditions  of 
the  seen.  It  is  this  deductive  function  of  the 
imagination  that  gives  to  it  a  strictly  logical  sig- 
nificance. For  instance.  Professor  Tyndall's  reason- 
ing concerning  the  Erith  church  Avas  somewhat  as 
follows:  The  windows  are  all  bent  inward,  there- 
fore the  pressure  must  have  operated  on  all  sides 
from  without,  inward;  such  pressure  could  only 
occur  upon  the  supposition  that  the  sound-waves, 
separating  right  and  left,  wholly  encompassed  the 
church,  etc.  In  each  case,  that  which  he  pictured 
to  his  mind  as  happening,  was  regarded  by  him  as 
actually  necessitated  by  the  facts  as  observed. 

Professor  Tyndall  has  most  admirably  discussed 
the  "Scientific  Use  of  the  Imagination;"  and  his 
lecture  under  that  title  every  student,  both  of  logic 
or  of  science,  should  read.  I  quote  one  passage 
from  it,  which  has  special  bearing  upon  what  has 
just  been  said :  "  We  are  gifted  with  the  power  of 
Imagination,  —  combining  what  the  Germans  call 
Anschauungsgabe  and  Einhildungskraft,  —  and  by 
this  power  we  can  lighten  the  darkness  which  sur- 
rounds the  world  of  the  senses.  There  are  tories 
in  science  who  regard  imagination  as  a  faculty  to 
be  feared  and  avoided  rather  than  employed.  They 
had  observed  its  action  in  weak  vessels  and  were 
unduly  impressed  by  its  disasters.  But  they  might 
with  equal  justice  point  to  exploded  boilers  as  an 


186  iNDtrCTlVE  LOGIC 

argument  against  the  use  of  steam.  Bounded  and 
conditioned  by  co-operant  Reason,  imagination  be- 
comes the  mightiest  instrument  of  the  scientific  dis- 
coverer. Newton's  passage  from  a  falling  apple 
to  a  falling  moon  was,  at  the  outset,  a  leap  of  the 
imagination.  When  William  Thomson  tries  to 
place  the  ultimate  particles  of  matter  between  his 
compass  points,  and  to  apply  to  them  a  scale  of 
millimetres,  he  is  powerfully  aided  by  this  faculty. 
And  in  much  that  has  been  recently  said  about 
protoplasm  and  life,  we  have  the  outgoings  of  the 
imagination  guided  and  controlled  by  the  known 
analogies  of  science.  In  fact,  without  this  power 
our  knowledge  of  nature  would  be  a  mere  tabula- 
tion of  coexistences  and  sequences.  We  should 
still  believe  in  the  succession  of  day  and  night,  of 
summer  and  winter;  but  the  soul  of  Force  would 
be  dislodged  from  our  universe;  causal  relations 
would  disappear,  and  with  them  that  science 
which  is  now  binding  the  parts  of  nature  to  an 
organic  whole."  ^ 

In  all  the  illustrations  which  have  been  given, 
and,  in  fact,  in  all  examples  of  the  framing  of 
hypotheses,  it  will  be  seen  that  the  mental  functions 
specially  in  operation  are  those  of  analysis  and 
synthesis,  —  a  separation  of  the  elements  as  far  as 
possible  into  their  simplest  forms  of  expression, 
and  the  building  them  together  into  some  one  sys- 
tem whose  unity  lies  in  the  assumed  hypothesis. 
Mr.  Venn  has  especially  emphasized  this  aspect  of 

1  Tyndall,  Use  and  Limit  of  the  Imagination  in  Science, 
p.  16. 


HYPOTHESIS  187 

hypothesis,  and  his  chapter  on  this  subject  will 
well  repay  a  careful  reading.^ 

Every  supposition,  however,  is  not  necessarily  an 
hypothesis  in  the  logical  or  scientific  significance 
of  that  term.  It  will  be  necessary,  therefore,  to 
mention  some  of  the  requirements  which  a  logical 
hypothesis  should  satisfy. 

1.  An  hypothesis  should  be  plausible  ;  that  is,  it 
should  be  no  fanciful,  or  merely  conjectural,  expla- 
nation of  the  phenomena  in  question.  The  sup- 
positions of  the  interference  of  spirits,  or  in  a 
mythological  age  of  the  gods,  to  account  for  per- 
plexing situations  or  obscure  happenings,  have  no 
rank  as  hypotheses  ;  so,  also,  Fate  is  often  referred 
to  as  a  convenient  confession  of  ignorance  in  lieu  of 
a  satisfactory  explanation.  Spinoza  has  remarked 
upon  this  as  follows :  "  They  who  have  desired  to 
find  scope  for  the  display  of  their  ingenuity  in 
assigning  causes,  have  had  recourse  to  a  new  style 
of  argument  to  help  them  in  their  conclusions, 
namely,  by  reduction,  not  to  the  impossible  or  ab- 
surd, but  to  ignorance  or  the  unknown,  a  procedure 
which  shows  very  plainly  that  there  was  no  other 
course  open  to  them." 

The  difference  between  a  scientific  hypothesis 
and  a  popular  explanation  concerning  the  same 
phenomena  may  be  found  in  Darwin's  account  of 
"a  strange  belief  which  is  general  amongst  the 
inhabitants  of  the  Maldiva  atolls,  namely,  that 
corals  have  roots,  and  therefore  that  if  merely 
broken  down  to  the  surface,  they  grow  up  again ; 

1  Venn,  Empirical  Logic,  Chapter  XVI. 


188  INDUCTIVE  LOGIC 

but  if  rooted  out,  they  are  permanently  destroyed. 
By  this  means  the  inhabitants  keep  their  harbors 
clear ;  and  thus  the  French  governor  of  St.  Mary's 
in  Madagascar  'cleared  out  and  made  a  beautiful 
little  port  at  that  place.' "  ^  Their  explanation, 
however,  is  purely  fanciful,  having  no  basis  in  fact. 
In  contrast,  Darwin's  hypothesis  to  explain  the 
facts  in  the  case  is  of  a  logically  scientific  nature, 
and  is  as  follows :  Inasmuch  as  loose  sediment  is 
injurious  to  the  living  polypifers,  and  as  it  is  prob- 
able that  sand  would  accumulate  in  the  hollows 
formed  by  tearing  out  the  corals,  but  not  on  the 
broken  and  projecting  stumps,  therefore  in  the 
former  case  the  fresh  growth  of  coral  might  be 
thus  prevented  by  the  deposited  sediment. 

2.  The  second  requirement  is  that  the  hypothesis 
must  be  capable  of  proof  or  disproof.  This  does 
not  demand  a  test  by  experiment  necessarily ;  for 
that,  as  we  have  seen,  may  be  impossible.  It  does, 
however,  require  that  some  facts  should  be  forth- 
coming that  will  either  confirm  the  hypothesis  or 
disprove  it.  There  are  cases,  however,  as  Lotze 
suggests,  whose  very  nature  precludes  the  possi- 
bility of  proving  or  disproving  the  hypothesis 
framed  to  account  for  them.  For  instance,  the 
very  common  and  simple  hypothesis  of  regarding 
the  stars,  which  are  apparently  but  small  points  of 
light,  as  bodies  of  vast  size,  only  very  remote  from 
us,  is  in  itself  incapable  of  being  either  refuted  or 
confirmed  by  subsequent  discovery.  Lotze  says : 
"We   must   abide   content  if   our   hypotheses   are 

1  Darwiu,  Cofcd  Reefs,  p.  89. 


HYPOTHESIS  189 

thinkable  and  useful,  if  they  are  capable  of  ex- 
plaining all  interconnected  appearances,  even  such 
as  were  still  unknown  when  we  constructed  them, 
if,  that  is  to  say,  they  are  indirectl}^  confirmed  by 
the  agreement  of  all  that  can  be  deduced  from  them 
in  thought  with  the  actual  progress  of  experience. 
But  if  we  would  be  so  fortunate  as  to  find  an 
hypothesis  which  will  not  lack  this  subsequent 
confirmation,  we  must  not  simply  assume  anything 
that  can  be  barely  conceived  as  real ;  we  must  only 
assume  that  which,  besides  being  thinkable,  con- 
forms, so  to  speak,  to  the  universal  customs  of  real- 
ity, or  to  the  special  local  customs  which  prevail  in 
that  department  of  phenomena  to  which  the  object 
we  are  investigating  belongs."  ^ 

It  is  to  be  specially  observed  that  while  the  re- 
quirement of  proof  of  an  hypothesis  may  be  waived 
in  the  sphere  of  phenomena  where  proof  is  mani- 
festly impossible,  still,  where  proof  is  available,  an 
hypothesis  must  never  be  so  framed  as  to  render 
the  required  test  either  impossible  or  impracticable. 

3.  The  hypothesis  must  be  adequate.  It  must 
cover  all  the  facts  in  the  case.  An  outstanding 
fact  which  it  cannot  explain  is  sufiicient  to  contro- 
vert such  an  hypothesis.  A  knowledge  of  the  dis- 
tinction between  postulate  and  hypothesis,  and  of 
the  relation  which  nominally  exists  between  the  two, 
will  help  us  to  appreciate  more  clearly  the  force 
of  this  requirement  of  adequacy.  As  defined  by 
Lotze,  a  postulate  "expresses  the  conditions  which 
must  be  set  up,  or  the  ground  of  explanation  which 
1  Lotze,  Logic,  p.  353. 


190  INDUCTIVE  LOGIC 

must  be  given  by  some  reality,  force,  or  event,  before 
we  can  think  the  phenomenon  in  the  form  in  which 
it  is  presented  to  us ;  it  thus  requires  or  postulates 
the  presence  of  something  that  can  account  for  the 
given  effect.  An  hypothesis  is  a  conjecture  which 
seeks  to  fill  up  the  postulate  thus  abstractly  stated 
by  specifying  the  concrete  causes,  forces,  or  pro- 
cesses out  of  which  the  phenomenon  really  arose 
in  this  particular  case,  while  in  other  cases  maybe 
the  same  postulate  is  to  be  satisfied  by  utterly  dif- 
ferent though  equivalent  combinations  of  forces  or 
active  elements."  ^  According  to  this  distinction 
as  applied  to  the  problem  of  the  source  of  the 
sun's  energy,  the  postulate  would  be  the  sum  of 
conditions  which  require  explanation;  namely,  the 
tremendous  radiation  of  heat  extending  through 
thousands  and  thousands  of  years.  The  postulate 
therefore  requires  a  force  adequate  to  supply  for  so 
long  a  period  so  great  an  amount  of  energy.  We 
found  that  ordinary  combustion  of  the  most  highly 
combustible  materials  would  not,  as  an  hypothesis, 
satisfy  the  conditions  which  obtain  in  the  postulate ; 
nor  would  the  liberation  of  chemical  energy  stand 
as  an  hypothesis  adequate  to  satisfy  the  postulate ; 
the  hypothesis  of  impact  of  masses  upon  the  sun's 
surface  from  immense  distances  presents  a  force 
sufficient  to  meet  the  requirements  of  the  postulate. 
Moreover,  we  see  in  this  illustration  how  the  hy- 
pothesis is  a  particular  and  concrete  expression  of 
the  conditions  expressed  in  general  and  in  abstract 
terms  in  the  postulate.     The  essential  characteristic 

1  Lotze,  Logic,  pp.  349,  350. 


HYPOTHESIS  191 

therefore  of  the  hypothesis  is  that  it  shall  perfectly 
satisfy  all  the  conditions  expressed  in  the  xjostulate. 

The  hypothesis  that  nature  abhorred  a  vacuum,  in 
order  to  account  for  the  rise  of  water  in  a  tube  or 
pump,  was  seen  to  break  down  utterly  when  it  was 
found  that  the  water  did  not  rise  beyond  some 
thirty-three  feet.  The  demand  of  the  postulate  in 
the  case  was  a  force  of  precisely  such  magnitude 
that  it  would  balance  a  column  of  water  thirty-three 
feet  in  height.  This  force,  precisely  satisfying  the 
conditions  of  the  postulate,  is  found  in  the  hypoth- 
esis that  the  atmospheric  pressure  is  such  a  magni- 
tude as  to  exert  a  pressure  equivalent  to  a  column 
of  water  some  thirty-three  feet  in  height.  The 
strength  of  the  hypothesis  lies  in  its  exact  and 
appropriate  fitting  into  the  facts  of  the  problem. 

Another  illustration  of  the  fitting  of  hypothesis 
to  postulate,  and  one  where  the  conditions  of  the 
postulate  are  extremely  complex,  I  have  chosen 
from  Mr.  Wallace's  work.  On  Natural  Selection: 
"  There  is  a  Madagascar  orchis  —  the  Angrmcum 
sesqiiipedale  —  with  an  immensely  long  and  deep 
nectary.  How  did  such  an  extraordinary  organ 
come  to  be  developed  ?  Mr.  Darwin's  explanation 
is  this.  The  pollen  of  this  flower  can  only  be 
removed  by  the  base  of  the  proboscis  of  some  very 
large  moths,  when  trying  to  get  at  the  nectar  at  the 
bottom  of  the  vessel.  The  moths  with  the  longest 
probosces  would  do  this  most  effectually;  they 
would  be  rewarded  for  their  long  tongues  by  get- 
ting the  most  nectar ;  whilst,  on  the  other  hand,  the 
flowers  with  the  deepest  nectaries  would  be  the  best 


192  INDUCTIVE  LOGIC 

fertilized  by  the  largest  moths  preferring  them. 
Consequently  the  deepest-nectaried  orchids  and  the 
longest-tongued  moths  would  each  confer  on  the 
other  an  advantage  in  the  battle  of  life.  This 
would  tend  to  their  respective  perpetuation,  and 
to  the  constant  lengthening  of  nectaries  and  pro- 
bosces.  In  the  Angrcecum  sesquipedale  it  is  neces- 
sary that  the  proboscis  should  be  forced  into  a 
particular  part  of  the  flower,  and  this  would  only 
be  done  by  a  large  moth  burying  its  proboscis  to 
the  very  base,  and  straining  to  drain  the  nectar 
from  the  bottom  of  the  long  tube,  in  which  it  occu- 
pies a  depth  of  one  or  two  inches  only.  Now  let 
us  start  from  the  time  when  the  nectary  was  only 
half  its  present  length,  or  about  six  inches,  and  was 
chiefly  fertilized  by  a  species  of  moth  which  ap- 
peared at  the  time  of  the  plant's  flowering,  and 
whose  proboscis  was  of  the  same  length.  Among 
the  millions  of  flowers  of  the  Angra^cum  produced 
every  year,  some  would  always  be  shorter  than  the 
average,  some  longer.  The  former,  owing  to  the 
structure  of  the  flower,  would  not  get  fertilized, 
because  the  moths  could  get  all  the  nectar  without 
forcing  their  trunks  down  to  the  very  base.  By 
this  process  alone  the  average  length  of  the  nec- 
tary would  annually  increase,  because  the  short- 
nectaried  flowers  being  sterile,  and  the  long  ones 
having  abundant  offspring,  exactly  the  same  effect 
would  be  produced  as  if  a  gardener  destroyed  the 
short  ones,  and  sowed  the  seed  of  the  long  ones 
only ;  and  this  we  know  by  experience  would  pro- 
duce a  regular  increase  of  length,  since  it  is  this 


HYPOTHESIS  193 

very  process  which  has  increased  the  size  and 
changed  the  form  of  our  cultivated  fruits  and 
floAvers.  But  this  would  lead  in  time  to  such  an 
increased  length  of  the  nectary  that  many  of  the 
moths  could  only  just  reach  to  the  surface  of  the 
nectar,  and  only  the  few  with  exceptionally  long 
trunks  be  able  to  suck  up  a  considerable  portion. 
This  would  cause  many  moths  to  neglect  these  flow- 
ers, because  they  could  not  get  a  satisfying  supply 
of  necta.r,  and  if  these  were  the  only  moths  in  the 
country  the  flowers  would  undoubtedly  suffer,  and 
the  further  growth  of  the  nectary  be  checked  by 
exactly  the  same  process  which  had  led  to  its 
increase. 

"  But  there  are  an  immense  variety  of  moths,  of 
various  lengths  of  proboscis,  and  as  the  nectary 
became  longer,  other  and  larger  species  would  be- 
come the  fertilizers,  and  would  carry  on  the  process 
till  the  largest  moths  became  the  sole  agents.  Now, 
if  not  before,  the  moth  would  also  be  affected ;  for 
those  with  the  longest  probosces  would  get  the  most 
food,  would  be  the  strongest  and  most  vigorous, 
would  visit  and  fertilize  the  greatest  number  of 
flowers,  and  would  leave  the  largest  number  of 
descendants.  The  flowers  most  completely  fertil- 
ized by  these  moths  being  those  which  had  the 
longest  nectaries,  there  would  in  each  generation 
be,  on  the  average,  an  increase  in  the  length  of  the 
nectaries,  and  also  an  average  increase  in  the  length 
of  the  probosces  of  the  moths ;  and  this  would  be  a 
7iecessary  result  from  the  fact  that  nature  ever  fluct- 
uates about  a  mean,  or  that  in  every  generation 


194  INDUCTIVE  LOGIC 

there  would  be  flowers  with  longer  and  shorter 
nectaries,  and  moths  with  longer  and  shorter  pro- 
bosces  than  the  average.  I  may  here  mention  that 
some  of  the  large  Sphinx  moths  of  the  tropics  have 
probosces  nearly  as  long  as  the  nectary  of  Angroi- 
cum  sesquipedale.  I  have  carefully  measured  the 
proboscis  of  a  specimen  of  Macrosila  duentius  from 
South  America,  in  the  collection  of  the  British 
Museum,  and  find  it  to  be  nine  inches  and  a  quarter 
long.  One  from  tropical  Africa  {Macrosila  mor- 
gayiii)  is  seven  inches  and  a  half.  A  species  having 
a  proboscis  two  or  three  inches  longer  could  reach 
the  nectar  in  the  longest  flowers  of  Angrmcum  ses- 
quipedale, whose  nectaries  vary  in  length  from  ten 
to  fourteen  inches.  That  such  a  moth  exists  in 
Madagascar  may  be  safely  predicted ;  ^  and  natural- 
ists who  visit  that  island  should  search  for  it  with 
as  much  confidence  as  astronomers  searched  for 
the  planet  Nejotune,  —  and  I  venture  to  predict 
they  will  be  equally  successful."  ^ 

I  have  given  this  quotation  at  length  in  order  to 
indicate  not  only  the  fitting  of  hypothesis  to  the 
facts  observed,  but  also  the  large  and  important 
part  performed  by  the  imagination  in  reproducing 
along  parallel  lines  the  natural  history  of  the  orchid 
and  moth.  The  hypothesis  reaches  back  over  an 
indefinitely  long  past,  by  virtue  of  the  necessities 

1  It  is  interesting  to  note  that  since  Mr,  Wallace  wrote  the 
above,  Kirby,  in  his  European  Moths  and  Butterflies,  makes 
mention  of  one  of  the  Sphingidae  with  a  proboscis  tivelve  inches 
long! 

2  Wallace,  On  Natw^al  Selection,  pp.  271-275. 


HYPOTHESIS  195 

observed  in  the  present,  and  in  accordance  with 
well-established  analogies  and  approved  inductions. 
The  function  of  the  imagination  especially  promi- 
nent is  that  of  its  deductive  insight,  which  is  able 
to  picture  to  the  mind  the  inevitable  results  of  this 
and  that  condition  as  furnished  by  the  postulate, 
and  then  to  fit  such  necessitated  results  into  one  self- 
consistent  system,  with  nothing  left  unexplained, 
incongruous,  or  contradictory. 

Another  illustration  of  an  hypothesis  covering  a 
large  number  of  complex  facts  is  that  of  the  ferti- 
lization of  certain  flowers  by  means  of  the  wind. 
As  given  by  Sir  John  Lubbock,  we  have  the  follow- 
ing facts  and  the  corresponding  explanation  of 
them :  "  Wind-fertilized  flowers,  as  a  rule,  have  no 
color,  emit  no  scent  and  produce  no  honey,  and  are 
regular  in  form.  Color,  scent,  and  honey  are  the 
three  characteristics  by  which  insects  are  attracted 
to  flowers.  Again,  as  a  rule  wind-fertilized  flowers 
produce  much  more  pollen  than  those  which  are 
fertilized  by  insects.  This  is  necessary,  because 
it  is  obvious  that  the  chances  against  any  given 
pollen  grain  reaching  the  stigma  are  much  greater 
in  the  one  case  than  in  the  other.  Every  one  has 
observed  the  showers  of  yellow  pollen  produced  by 
the  Scotch  fir.  Again,  it  is  an  advantage  to  wind- 
fertilized  plants  to  flower  early  in  the  spring  before 
the  leaves  are  out,  because  the  latter  would  catch 
much  of  the  pollen,  and  thus  interfere  with  its 
access  to  the  stigma.  Again,  in  these  plants  the 
pollen  is  less  adherent,  so  that  it  can  be  easily 
blown  away  by  the  wind,  which  would  be  a  disad- 


196  INDUCTIVE  LOGIC 

vantage  in  most  plants  which  are  fertilized  by 
insects.  Again,  such  flowers  generally  have  the 
stigma  more  or  less  branched,  or  hairy,  which  evi- 
dently must  tend  to  increase  their  chances  of 
catching  the  pollen."^  There  is  here  a  structural 
adaptation  of  these  plants  to  the  circumstances 
designed  to  explain  them,  so  that  the  consequent 
self-consistent  system  thus  formed  carries  with  it 
the  weight  of  conviction. 

There  are  some  explanations  which  do  not  per- 
fectly correspond  to  reality,  and  yet,  when  their 
nature  is  known,  they  may  be  profitably  used,  not 
to  represent  reality,  but  to  assist  the  mind  by  an 
approximate  representation  to  better  appreciate  the 
facts  as  they  really  are  related  one  to  another. 
These  so-called  "  fictions  "  are  useful,  especially  in 
mathematics.  We  suppose,  for  instance,  inscribed 
and  circumscribed  polygons  of  a  circle,  with  ever- 
increasing  number  of  sides,  gradually  approaching 
and  becoming  coincident  finally  with  the  curve 
itself.  This  latter  we  know  to  be  impossible,  and 
yet  we  may  treat  that  which  hai^pens  only  approxi- 
mately as  though  really  happening,  merely  as  an 
aid  to  the  imagination ;  and  a  fiction,  if  always  so 
understood,  may  thus  prove  helpful  in  the  repre- 
sentation of  reality  more  clearly  to  our  minds. 

4.  The  hypothesis,  moreover,  should  involve  no 
contradiction.  This  is  clearly  a  requirement  that 
is  deductive  rather  than  inductive,  depending  upon 
the  fundamental  principle  of  contradiction  lying  at 
the  basis  of  the  deductive  system  of  logic. 
1  Lubbock,  Scientific  Lectures,  pp.  9, 10. 


HYPOTHESIS  197 

5.  The  hypothesis  should  be  as  simple  as  possible. 
No  involved  explanation  that  mystiiies  rather  than 
clears  the  difficulties  presented  can  rank  as  a  true 
hypothesis.  Simplex  vert  sigillum.  This  require- 
ment, of  course,  cannot  in  all  cases  be  strictly  com- 
plied with ;  for  the  phenomena  to  be  explained  may 
present  such  a  degree  of  complexity  that  a  simple 
hypotliesis  would  be  altogether  out  of  the  question. 
For  instance,  the  hypothesis  of  a  substance  filling 
the  universe,  and  pervading  all  particles  of  matter, 
however  solid  and  closely  knit  together,  a  substance 
itself  more  solid  than  steel,  and  more  elastic  as  well, 
such  a  supposition  seems  not  only  too  involved,  but 
also  even  to  belie  the  ordinary  judgments  of  common 
sense.  And  yet  this  undulatory  hypothesis  is  more 
and  more  confirmed  by  every  advance  of  science  in 
tlie  knowledge  of  the  phenomena  of  light  and  heat. 

It  sometimes  happens  that  the  very  failure  of  an 
hypothesis  forms  a  substantial  contribution  to  the 
progress  of  thought,  leading  to  the  readjustment  of 
a  received  theory,  or  stimulating  research  in  order 
to  discover  the  true  in  place  of  the  false  hypothesis. 
As  Mr,  Tait  says :  '^  We  all  know  that  if  there 
had  not  been  a  pursuit  after  the  philosopher's  stone, 
chemistry  could  not  yet  have  been  anything  like  the 
gigantic  science  it  now  is.  In  the  same  way  we  can 
say,  that  modern  physics  could  not  yet  have  covered 
the  ground  it  now  occupies  had  it  not  been  for  this 
experimental  seeking  for  the  so-called  perpetual 
motion,  and  the  consequent  establishment  of  a  defi- 
nite and  scientifically  useful  negative."  ^     The  cir- 

1  Tait,  Recent  Advances  in  Physical  Science,  p.  69. 


198  INDUCTIVE  LOGIC 

cular  theory  of  the  orbits  of  the  planets,  while 
incorrect,  yet  made  the  transition  easier  from  the 
hypothesis  of  circular  motion  to  that  of  motion  in 
an  elliptical  orbit,  which  is  the  true  theory.  It 
often  happens  that  an  hypothesis  may  not  be 
wholly  wrong  but  may  need  correction,  and  this  is 
often  provided  for,  not  by  a  total  rejection  of  the 
hypothesis  in  question,  but  by  supplementing  it  by 
so-called  subsidiary  hypotheses. 

As  to  the  tests  of  a  correct  hypothesis  in  addition 
to  the  fulfilment  of  the  requirements  already  men- 
tioned. Dr.  Whewell  has  especially  emphasized  the 
importance  of  what  he  has  styled  a  ^^  Consilience  of 
Inductions."  An  hypothesis  receives  a  confirmatory 
strengthening  of  its  validity,  when  it  enables  us  to 
explain  and  determine  cases  not  only  of  the  same 
kind  as  the  phenomena  out  of  which  the  hypothe- 
sis itself  has  developed,  but  cases  which  arise  in 
a  sphere  entirely  different  from  that  which  gave 
material  originally  for  the  formation  of  the  hy- 
pothesis. An  hypothesis  that  can  thus  be  carried 
into  new  territory  as  an  effective  instrument  of 
research,  is  thereby  doubly  accredited.  As  Dr. 
Whewell  remarks:  "Accordingly  the  cases  in 
which  inductions  from  classes  of  parts  altogether 
diiferent  have  thus  jumped  together,  belong  only  to 
the  best  established  theories  which  the  history  of 
science  contains.  And  as  I  shall  have  occasion  to 
refer  to  this  peculiar  feature  in  their  evidence,  I 
will  take  the  liberty  of  describing  it  by  a  particular 
phrase ;  and  will  term  it  the  Consilience  of  Liduc- 
tions.     It  is  exemplified  principally  in  some  of  the 


HYPOTHESIS  199 

greatest  discoveries.  Thus  it  was  found  by  Newton 
that  the  doctrine  of  the  attraction  of  the  sun  vary- 
ing according  to  the  inverse  square  of  the  distance, 
which  explained  Kepler's  Tliird  Law,  of  the  pro- 
portionality of  the  cubes  of  the  distances  to  the 
squares  of  the  periodic  times  of  the  planets,  ex- 
plained also  his  First  and  Second  Laivs,  of  the 
elliptical  motion  of  each  planet;  although  no 
connection  of  these  laws  had  been  visible  before. 
Again,  it  appeared  that  the  force  of  universal  gravi- 
tation, which  had  been  inferred  from  the  perturba- 
tions of  the  moon  and  planets  by  the  sun  and  by 
each  other,  also  accounted  for  the  fact,  apparently 
altogether  dissimilar  and  remote,  of  the  precessioyi 
of  the  equinoxes.  Here  was  a  most  striking  and 
surprising  coincidence  which  gave  to  the  theory  a 
stamp  of  truth  beyond  the  power  of  ingenuity  to 
counterfeit."  ^ 

When  two  rival  hypotheses  can  be  submitted  to 
the  test  of  an  experiment  which  negatives  one  and 
confirms  the  other,  such  a  testing  is  called  an  ex- 
perimentum  crucis.  The  name  was  first  given  by 
Bacon,  and  "has  met  with  universal  acceptance  in 
scientific  phraseology.  A  crucial  test,  as  decisive 
between  the  emission  and  the  undulatory  theory 
of  light,  is  given  in  an  experiment  first  tried  by 
Father  Grimaldi,  a  Bolognese  monk,  in  1665.  If 
a  shutter  be  pierced  with  a  very  small  hole,  and 
the  luminous  cone  which  passes  through  the  orifice 
be  examined,  the  cone  will  be  found  to  be  much 

1  WTaewe]],  Novum  Organon  Renovatum,  Bk.  H.  Ch.  V, 
Art.  110. 


200  iNDtfCTIVE  LOGIC 

less  acute  than  would  be  expected,  considering  only 
the  rectilinear  transmission  of  the  rays,  as  according 
to  the  emission  theory.  If  there  be  interposed  in 
the  path  of  the  luminous  ray  a  second  shutter, 
pierced  with  a  hole  also,  it  will  be  noticed  that  the 
rays  of  the  second  cone  are  even  more  divergent 
than  those  of  the  first.  If  the  image  of  the  orifice 
be  received  upon  a  screen,  a  white  circle  is  seen 
surrounded  by  a  dark  ring,  next  a  white  ring,  even 
more  brilliant  than  the  central  portion,  then  a  second 
dark  ring,  and  finally  another  very  faint  white  ring. 
If  in  the  shutter  with  which  the  experiment  is 
made,  two  very  suiall  holes  are  pierced  at  a  dis- 
tance from  each  other  of  one  or  two  millimetres, 
and  the  two  images  received  upon  a  screen  in  such 
a  manner  that  they  overlap  each  other,  it  is  found 
that  in  the  cuticular  segment  formed  by  the  over- 
lapping of  the  images,  the  circles  are  more  obscure 
than  in  the  part  where  they  are  separated.  Thus 
by  adding  light  to  light  darkness  is  produced.^ 
These  phenomena  are  now  known  to  be  consistent 
only  with  the  nndulatory  theory,  and  directly  in 
contradiction  to  the  emission  hypothesis. 

M.  Komanes  performed  several  experiments  upon 
bees  which  had  the  force  of  crucial  tests  of  two 
opposed  hypotheses,  one,  that  bees  possess  a  general 
sense  of  direction,  irrespective  of  any  special  knowl- 
edge of  their  particular  surroundings;  the  other, 
that  they  are  guided  in  their  flight  by  a  knowledge 
of  the  localities  which  they  have  been  wont  to  fre- 
quent. M.  Eomanes  took  a  score  of  bees  in  a  box  out 
1  Saigey,  The  Unity  of  Natural  Phenomena,  p.  &o. 


HYPOTHESIS  201 

to  sea,  where  there  coukl  be  no  landmarks  to  guide 
the  insects  home.  None  of  them  returned  home. 
Then  he  liberated  a  second  lot  of  bees  on  the  sea- 
shore, and,  none  of  these  returning,  he  liberated 
another  lot  on  the  lawn  between  the  shore  and  the 
house.  None  of  these  returned,  although  the  dis- 
tance from  the  lawn  to  the  hive  was  not  more  than 
two  hundred  yards.  Lastly,  he  liberated  bees  in 
different  parts  of  the  flower-garden  on  either  side 
of  the  house,  and  these  at  once  returned  to  the 
hive;  and  with  repetition  of  the  experiment,  a 
similar  result,  even  arriving  at  the  hive  before 
he  himself  had  time  to  run  from  the  place  where 
he  had  liberated  them  to  the  hive.  As  the  garden 
was  a  large  one,  many  of  them  had  to  fly  a  greater 
distance,  in  order  to  reach  the  hive,  than  those 
liberated  on  the  front  lawn.  Their  uniform  suc- 
cess, therefore,  in  finding  their  way  home  so  im- 
mediately was  no  doubt  due  to  their  special 
knowledge  of  the  flower-garden,  and  not  to  any 
general  sense  of  direction.^ 

The  hypothesis  that  leads  to  verification  by  ex- 
periment represents  true  scientific  procedure,  and 
that  which  has  actually  been  the  most  effective 
instrument  of  research  in  all  the  various  spheres  of 
human  investigation.  The  old  controversy  between 
Mill  and  Whewell  admits  of  a  ready  adjustment  in 
this  regard.  Whewell  emphasized  discovery  as  the 
heart  of  the  system  of  induction,  leading  to  the 
framing  of   hypotheses  whose  chief  test  was  not 

1  Lubbock,  On  the  Senses,  Instincts,  and  Intelligence  of 
Animals,  pp.  269,  270. 


202  INDUCTI\'E  LOGIC 

experimental  so  much  as  the  capability  of  account- 
ing for  the  given  phenomena.  Mill,  on  the  other 
hand,  insisted  that  logic  was  essentially  proof,  and 
not  discovery.  He,  accordingly,  emphasized  the 
experimental  testing  by  means  of  his  several  meth- 
ods, as  being  the  all-important  part  of  the  in- 
ductive method.  He  had  little  concern  for  the 
origin  of  the  suggestions  as  to  the  most  likely 
causal  elements  in  the  midst  of  a  complex  phe- 
nomenon. The  primary  function  of  logic,  according 
to  him,  is  merely  to  prove  or  disprove.  The  ideas 
of  Whewell  and  Mill  are  not  necessarily  contradic- 
tory; they  can  be  regarded  as  mutually  supple- 
mentary, which  gives  us  a  true  account  of  the  ideal 
logical  method,  where  hypothesis  suggests  the  line 
of  experiment,  and  experiment  in  turn  confirms 
hypothesis.  In  such"  a  method,  as  can  be  seen  in 
the  illustration  given,  there  is  a  blending  of  deduc- 
tive and  inductive  reasoning,  which  is  the  general 
characteristic  of  all  actual  processes  of  thought. 
As  Sigwart  has  so  admirably  put  it:  '-'Without 
quickness  of  combination,  by  which  we  can  call  up 
a  number  of  possible  analogies  and  apply  them  to 
the  unexplained  case;  without  a  happy  power  of 
divination  which  is  guided  by  unanalyzable  associa- 
tions to  discover  that  analogy  which  embraces  most 
aspects  of  the  event;  finally,  without  imagination 
to  construct  connections  for  which  the  only  ground 
may  be  a  hidden  similarity,  our  thoughts,  if  com- 
pelled to  proceed  strictly  according  to  method,  would 
frequently  be  condemned,  by  the  impossibility  of 
discovering  in  this  way  a  sufficiently  grounded  con- 


HYPOTHESIS  ^03 

nection,  to  comi^lete  stagnation.  But  the  fact  is  in 
no  way  contrary  to  the  nature  of  induction ;  it  is  a 
necessary  consequence  of  it.  We  cannot  even  begin 
the  process  of  inference  without  making  general 
assumptions ;  and  the  general  proposition  which  we 
get  by  summing  up  a  number  of  instances  is  really 
a  hypothesis,  to  which,  it  is  true,  we  are  led  clearly 
and  certainly  in  this  case.  But  between  these  most 
general  presuppositions,  upon  which  all  induction 
is  grounded,  and  the  simplest  cases  to  which  they 
can  be  applied,  there  is  a  wide  region  within  Avhich 
the  hypotheses  which  are  always  necessary  for  in- 
duction can  only  be  formed  tentatively,  in  order  to 
give  some  definite  direction  to  investigation,  to  serve 
in  our  analysis  of  phenomena  into  their  elements  as 
a  means  of  breaking  up  complete  phenomena  on  cer- 
tain lines,  and  to  invent  the  experiments  which  will 
make  it  possible  to  confirm  or  refute  an  opinion."  ^ 

1  Sigwart,  Logic,  Vol.  H.  p.  423. 


CHAPTER   XTV 
Analogy 

It  often  happens  that  the  cause  of  a  phenomenon 
is  disclosed  by  the  fact  that  the  cause  of  a  similar 
phenomenon  is  known,  and  the  inference  then  fol- 
lows that  the  similar  phenomena  have  similar 
causes.  Such  a  process  of  inference  is  determina- 
tion by  analogy.  Analogy,  considered  in  its  rela- 
tion to  the  inductive  processes,  occupies  a  twofold 
position.  In  the  first  place,  when  a  complex  phe- 
nomenon is  given,  as  preliminary  to  the  formation 
of  any  hypothesis,  as  to  the  probable  cause  which 
will,  in  turn,  lead  to  experimental  determination 
by  one  of  the  inductive  methods,  the  mind  instinc- 
tively examines,  with  sweeping  glance,  every  detail 
of  the  phenomenon  for  the  purpose  of  discovering 
some  familiar  features  that  may  prove  suggestive 
of  known  relations  and  functions  occurring  in  other 
spheres.  Analogical  suggestion,  therefore,  initiates 
every  inductive  inquiry. 

In  the  second  place,  in  every  inductive  general- 
ization there  is  an  extension  of  the  known  into 
unknown  regions,  by  virtue  of  the  principle  of 
analogy  expressed  in  what  we  may  style  its  limit- 
ing case.  For  instance,  when  we  have  examined 
204 


ANALOGY  205 

a  number  of  ^I's  and  find  them  always  character- 
ized by  the  mark  B,  and  then  by  generalization 
rise  to  the  proposition,  All  ^'s  are  B,  we  do  so  by 
reason  of  postulating  an  analogy  between  all  the 
individual  ^'s  of  so  strictly  an  accurate  nature,  that 
it  amounts  to  essential  identity.  I  have  therefore 
called  this  the  limiting  case  of  analogy ;  and  this 
resemblance  of  particulars  is  the  ground  of  all  uni- 
versals  whereby  they  manifest  an  identity  in  the 
midst  of  differences.  We  are  therefore  justified  in 
affirming  that  all  inductive  generalizations  present 
an  aspect  of  analogical  inference. 

Analogy,  considered  as  a  mental  process,  is 
grounded  in  the  law  of  similarity.  This  tendency 
of  noting  resemblance  makes  possible  the  extension 
of  knowledge.  The  formation  of  our  concepts  is, 
in  the  main,  an  analogical  procedure;  just  as  the 
generalization  of  an  universal  depends  upon  our 
discrimination  of  the  elements  which  are  similar 
from  those  which  are  different.  While  analogy 
thus  functions  in  all  the  logical  processes  of 
thought,  it  is  used  in  a  more  restricted  sense  to 
indicate  that  mode  of  inference  especially  which 
proceeds  from  a  number  of  observed  characteristics 
that  are  similar,  to  others  which  are  thereby  judged 
to  be  similar  also.  This  method  is  very  potent  as 
an  instrument  of  discovery.  In  1845,  Faraday  dis- 
covered the  magnetic  rotary  polarization  of  light ; 
by  analogical  reasoning,  Waitmann  in  the  following 
year  inferred  that  a  similar  result  would  be  attained 
with  a  beam  of  heat,  which  was  afterwards  experi- 
mentally verified.     The  so-called  "natural  kinds'' 


206  INDUCTIVE  LOGIC 

furnish  manifold  illustrations  of  conclusive  analo- 
gies. They  possess  numerous  properties,  some  of 
them  known  and  others  unknown.  Through  large 
groups  of  them  are  found  similar  characteristics 
side  by  side  with  manifest  differences,  and  yet  the 
similarities  are  so  striking  that  often,  wdien  new 
properties  are  discovered  in  certain  members  of  the 
group,  there  seems  to  be  ground  for  inferring  their 
existence  in  other  members  of  the  group  also. 
Certain  properties  known  to  exist  in  potassium  and 
sodium  were  inferred  to  be  present  in  rubidium  and 
caesium ;  the  carbonates  of  sodium  and  potassium 
are  not  decomposed  by  a  red  heat,  and  it  was  in- 
ferred that  the  same  would  prove  true  of  the  car- 
bonates of  rubidium  and  csesium ;  and  such  proved 
to  be  the  case.  Some  of  the  statements  which  are 
true  of  chlorine  are  found  to  be  true  of  bromine 
and  iodine.  Mr.  Gore,  having  found  the  molecu- 
lar change  in  antimony  electro-deposited  from  its 
chloride,  he  inferred  and  discovered  the  same  in 
that  deposited  from  its  bromide  and  iodide.  Sir 
Humphry  Davy,  having  discovered  that  potassium 
might  be  isolated  by  means  of  electrolysis,  imme- 
diately inferred  and  proceeded  to  prove  by  experi- 
ment that  it  would  be  possible  also  to  isolate  sodium 
and  other  substances  of  analogous  properties.^ 

The  principle  of  analogy  lies  at  the  basis  of  all 
classification,  the  separating  and  grouping  together 
in  appropriate  divisions  individuals  which  possess 
certain  salient  attributes  in  common. 

Professor  Jevons'  definition  of  classification  em- 

1  Gore,  The  Art  of  Scientific  Discovery,  p.  522. 


ANALOGY  207 

bodies  at  the  same  time  a  full  statement  of  its 
exact  logical  significance  as  an  instrument  of  re- 
search, and  therefore  I  give  it  in  full :  "  By  the 
classification  of  any  series  of  objects,  is  meant 
the  actual  or  ideal  arrangement  together  of  those 
which  are  alike  and  the  separation  of  those  which 
are  unlike,  the  purpose  of  this  arrangement  being, 
primarily,  to  disclose  the  correlations  or  laws  of 
union  of  properties  and  circumstances,  and  secon- 
darily, to  facilitate  the  operations  of  the  mind  in 
clearly  conceiving  and  retaining  in  the  memory  the 
characters  of  the  object  in  question."  ^  In  describ- 
ing the  purpose  of  classification,  the  latter  clause 
is  more  a  psychological  desideratum  than  logical ; 
the  former  specification  contains  its  logical  pur- 
pose ;  namely,  to  disclose  the  correlations  or  laws 
of  union  of  properties  and  circumstances.  This 
may  be  illustrated  in  the  grouping  together  of 
potassium,  sodium,  csesium,  rubidium,  and  lithium, 
and  calling  them  the  alkaline  metals.  This  was 
done  by  virtue  of  the  common  characteristics  in 
the  midst  of  their  individual  peculiarities ;  namely, 
they  all  combine  very  energetically  with  oxygen 
to  decompose  water  at  all  temperatures,  and  form 
strongly  basic  oxides,  which  are  highly  soluble  in 
water,  yielding  powerful  caustic  and  alkaline  hy- 
drates from  which  water  cannot  be  expelled  by 
heat;  their  carbonates  are  also  soluble  in  water, 
and  each  metal  forms  only  one  chloride.  The 
manifest  advantage  of  classifying  these  metals 
together  lies  in  its  suggestive  capacity,  as  we  have 
1  Jevons,  Principles  of  Science,  p.  677. 


208  INDUCTIVE  LOGIC 

already  noted  in  illustrations  above  given.  So 
many  observed  similarities  suggest  inferences  by 
analogy ;  wlien,  for  instance,  a  new  property  is 
discovered  in  any  one  or  two  of  the  metals  of  this 
class,  the  idea  immediately  suggests  itself  that  the 
same  property  may  possibly  extend  over  all  the 
metals  of  the  same  class.  Not  only  is  such  an  idea 
suggested,  but  along  with  it  there  exists  an  ante- 
cedent probability  respecting  its  solution  in  accord- 
ance with  the  suggestion  which  analogy  starts. 

An  excellent  illustration  of  the  practical  results 
attained  through  a  scientific  use  of  classification  is 
found  in  Mr.  Lockyer's  researches  on  the  sun.^  As 
a  guide  as  to  what  elements  to  look  for  in  the  sun's 
photosphere,  he  prepared  a  classification  of  elements 
according  as  they  had  or  had  not  been  traced  in 
the  sun,  together  with  a  detailed  statement  of  the 
chemical  nature  of  each  element.  He  was  then 
able  to  observe  that  the  elements  found  in  the  sun 
were,  for  the  most  part,  those  forming  stable  com- 
pounds with  oxygen.  He  then  inferred  that  the 
other  elements  which  were  known  to  form  stable 
compounds  with  oxygen  would,  in  all  probability, 
be  found  present  in  the  sun.  Starting  upon  this 
suggested  track,  he  succeeded  in  discovering  five 
such  metals. 

Analogical  inference  carries  special  weight  when 
it  is  based  upon  the  principle  of  teleology;  that 
is,  when  any  observed  phenomena  seem  to  possess 
structural  contrivances  adapted  to  ends,  in  some 
degree,  at  least,  similar  to  human  contrivances 
1  Quoted  by  Jevous  in  Principles  of  Science,  p.  676. 


ANALOGY 


209 


designed  to  produce  certain  proposed  ends.     When 
this  similarity  is  apparent,  it  suggests  the  possi- 
bility that  an  observed  contrivance  in  nature  may 
subserve  ends  beyond  the  possibility  of  observa- 
tion, and  which,  therefore,  may  be  inferred  really 
to  exist.     AVe  have  seen  that  the  ground  of   all 
inference  lies  in  the  representation  of  any  given 
phenomena   of   consciousness   as   cohering   in   one 
system,  which  comprehends  the  several  parts  in 
a  common  unity  of  such  a  nature  that,  knowing 
some  of  the  parts  and  their  relations,  we  infer  the 
character  and  function  of  other  parts  not  known, 
and  yet  which   that   already  known  necessitates. 
And  among  the  many  kinds  of  relation  that  may 
obtain  between  part  and  part,  or  part  and  whole, 
the  teleological  is  a  very  common  one,  and,  more- 
over, by  its  nature  necessitates  certain  consequences 
that  lie  beyond  the  sphere  of  observation,  and  yet, 
nevertheless,  may  very  properly  be  supplied  by  in- 
ference.    In  other  words,  the  causal  connections  in 
a  system  are  not  merely  those  of  an  efficient  or 
a  formal  cause;  they  may,  with  a  like  force  and 
suggestiveness,  be  considered  in  the  light  of  a  final 
cause;   that  is,  the  presence  of  means  adapted  to 
certain  ends,  or  of  organs  adapted  to  certain  neces- 
sary functions,  or  of  contrivances  of  a  mechanical 
nature  as  though  designed  for  a  specific  purpose. 

Janet  has  specially  emphasized  the  importance 
and  prevalence  of  this  kind  of  inference,  and,  as  an 
illustration  of  the  cogency  of  inference  based  upon 
finality,  he  urges  that  the  certitude  which  the  belief 
in  the  intelligence  of  our  fellow-men  gives  us  is 


210  INDUCTIVE  LOGIC 

based  upon  analogical  reasoning  of  this  type ;  and 
that,  moreover,  this  belief,  resting  upon  such  a  basis, 
is  one  of  the  strongest  beliefs  which  we  possess. 
He  says:  "Xow,  if  we  ask  ourselves  why  we 
suppose  that  other  men  think,  we  shall  see  that  it 
is  in  virtue  of  the  principle  of  final  causes.  In 
effect,  what  is  it  that  experience  shows  in  the 
actions  of  other  men,  but  a  certain  number  of 
phenomena  co-ordinated  in  a  certain  manner,  and 
bound  not  only  together,  but  also  to  a  future  phe- 
nomenon more  or  less  remote  ?  Thus  when  we  see 
a  man  prepare  his  food  by  means  of  fire,  we  know 
that  this  assemblage  of  phenomena  is  connected 
with  the  act  of  taking  food ;  when  we  see  a  painter 
drawing  lines  on  a  canvas,  we  know  that  these 
apparently  arbitrary  acts  are  connected  with  the 
execution  of  a  picture ;  when  we  see  a  deaf  mute 
making  signs  which  w^e  do  not  understand,  we  be- 
lieve that  these  gestures  are  connected  with  a  final 
effect,  w^hich  is  to  be  understood  by  him  to  whom 
he  makes  them ;  in  fine,  when  men  speak,  we  see 
that  the  articulations  of  which  a  phrase  is  com- 
l^osed  are  co-ordinated  to  each  other  so  as  to  pro- 
duce a  certain  final  effect,  which  is  to  awaken  in  us 
a  certain  thought  and  sentiment.  Now  we  cannot 
see  such  co-ordinations,  whether  actual  or  future, 
without  supposing  a  certain  cause  for  them ;  and 
as  we  know  by  internal  experience  that  with  our- 
selves such  co-ordinations  only  take  place  under 
the  condition  that  the  final  effect  is  previously 
represented  in  our  consciousness,  we  suppose  the 
same  thing  in  the  case  of  other  men;  in  a  word, 


ANALOGY  211 

we  suppose  for  them  the  consciousness  of  an  end, 
a  consciousness  reflecting  more  or  less,  according 
as  the  circumstances  more  or  less  resemble  those 
that  accompany  in  ourselves  the  reflecting  con- 
sciousness. Thus  when  we  affirm  the  intelligence 
of  other  men,  we  affirm  a  truth  of  indisputable  cer- 
titude ;  and  yet  we  only  affirm  it  on  the  ground  of 
analogy,  and  of  analogy  guided  by  the  principle  of 
final  causes."  ^ 

In  this  illustration  of  Janet's  we  have  the  idea 
of  a  system  of  co-ordinated  parts  especially  promi- 
nent; and  for  a  satisfactory  account  of  the  rela- 
tions obtaining  in  such  a  system,  it  will  be  seen 
how  indispensable  it  is  to  postulate  the  theory  of 
final  cause.  This  mode  of  inference  finds  a  striking 
illustration  in  the  famous  discovery  of  Harvey,  con- 
cerning the  circulation  of  the  blood.  In  the  early 
part  of  the  seventeenth  century,  while  Harvey  was 
his  pupil,  the  celebrated  anatomist,  Fabricius  Aqua- 
pendente  of  Padua,  observed  that  many  veins  con- 
tain valves  which  lie  open  as  long  as  the  blood  is 
flowing  towards  the  heart.  Harvey,  learning  of 
this  fact,  saw  in  it  the  suggestion  of  an  adaptation 
of  means  to  an  end ;  namely,  a  contrivance  so  fash- 
ioned by  nature  as  to  permit  the  blood  to  flow 
always  in  one  direction  only,  and  to  prevent  its 
flow  in  an  opposite  direction.  Observation  of  other 
portions  of  the  circulatory  mechanism  led  to  a  con- 
firmation of  the  idea,  and  to  the  discovery  of  the 
circulation  of  the  blood.^ 

1  Janet,  Final  Causes,  pp.  113, 114. 

2  Gore,  Art  of  Scientific  Discover]/,  p.  571. 


212  INDUCTIVE  LOGIC 

Again,  many  flint  substances  liave  been  discov- 
ered, as  though,  curiously  wrought,  with  sharp 
edges  and  a  place  as  though  designed  for  a  handle, 
with  which  to  wield  the  stone  as  a  weapon  or  a 
tool ;  it  has  been  inferred  from  these  general  char- 
acteristics that  the  stones  were  so  constructed  by 
human  effort,  and  used  by  human  beings  for  the 
purposes  for  which  they  evidently  seem  to  be 
adapted.  This  inference  is  based  upon  an  analogy 
between  the  peculiar  shapes  of  such  stones,  and 
known  shapes  designed  and  used  by  man. 

This  form  of  analogy  has  proved  specially  sug 
gestive  in  researches  regarding  plant  and  animal  life. 
Sir  John  Lubbock  gives  the  following  description  of 
the  common  white  dead-nettle,  with  the  explanation 
of  its  functions  that  is  evidently  a  teleological  in- 
ference: "The  flower  consists  of  a  narrow  tube, 
somewhat  expanded  at  the  upper  end,  where  the 
lower  lobe  of  the  corolla  forms  a  platform,  on  each 
side  of  which  is  a  small  projecting  lobe.  The  upper 
portion  of  the  corolla  is  an  arched  hood,  under 
which  lie  four  anthers  in  pairs,  while  between  them 
and  projecting  somewhat  downwards  is  the  pointed 
pistil.  At  the  lower  end,  the  tube  contains  honey, 
and  above  the  honey  is  a  row  of  hairs  almost  clos- 
ing the  tube.  Now,  why  has  the  flower  this  pecul- 
iar form  ?  What  regulates  the  length  of  the  tube? 
What  is  the  use  of  this  arch  ?  What  lessons  do 
these  lobes  teach  us  ?  What  advantage  is  the 
honey  to  the  flower  ?  Of  ichat  vse  is  the  fringe  of 
hairs  ?  AVhy  does  the  stigma  project  beyond  the 
anthers  ?     Why  is  the  corolla  white,  while  the  rest 


ANALOGY  213 

of  the  plant  is  green  ?  Similar  questions  may  of 
course  be  asked  with  reference  to  other  flowers. 
At  the  close  of  the  last  century,  Conrad  Sprengel 
published  a  valuable  work,  in  which  he  pointed  out 
that  the  forms  and  colors,  the  scent,  honey,  and 
general  structure  of  flowers,  have  reference  to  the 
visits  of  insects,  which  are  of  importance  in  trans- 
ferring the  pollen  from  the  stamens  to  the  pistil. 
Mr.  Darwin  developed  this  theory  and  proved  ex- 
perimentally that  the  special  service  which  insects 
perform  to  flowers,  consists  not  only  in  transferring 
the  pollen  from  the  stamens  to  the  pistil,  but  in 
transferring  it  from  the  stamens  of  one  flower  to 
the  pistil  of  another."  ^  The  line  of  subsequent  ob- 
servation and  experiment  was  thus  originally  sug- 
gested by  the  structural  appearance  of  these  flowers 
which  seemed  formed  for  some  specific  end.  The 
questions,  once  started,  —  To  what  end  ?  To  what 
purpose  ?  For  what  use  ?  —  led  to  the  theory  of 
Sprengel  and  the  corroborative  experiments  of 
Darwin. 

This  is  further  illustrated  in  some  very  inter- 
esting flower  structures,  also  described  by  Sir 
John  Lubbock,  which  indicate  peculiar  contrivances 
for  the  destruction  of  insects.  The  peculiarity  of 
formation  first  suggested  some  such  end  as  this, 
which  has  since  been  proved  by  careful  observation 
to  be  the  case.  "The  first  observation  on  insect- 
eating  flowers  was  made  about  the  year  1868  by 
Ellis.  He  observed  that  in  Dionaea,  a  North 
American   plant,  the   leaves   have  a  joint   in   the 

1  Lubbock,  Scientific  Lectures,  pp.  1,  2. 


214  iNDUCTm:  logic 

middle,  and  thus  close  over,  kill,  and  actually  di- 
gest any  insect  which  may  alight  on  them.  An- 
other case  is  that  of  Utricularia,  an  aquatic  species 
which  bears  a  number  of  utricles  or  sacs,  which 
have  been  supposed  to  act  as  floats.  Branches, 
however,  which  bear  no  bladders  float  just  as  well 
as  the  others,  and  there  seems  no  doubt  that  their 
real  use  is  to  capture  small  aquatic  animals,  which 
they  do  in  considerable  numbers.  The  bladders,  in 
fact,  are  on  the  principle  of  an  eel-trap,  having  an 
entrance  closed  with  a  flap,  which  permits  an  easy 
entrance,  but  effectually  prevents  the  unfortunate 
victim  from  getting  out  again.  In  the  genus,  Sar- 
racenia,  some  of  the  leaves  are  in  the  form  of  a 
pitcher.  They  secrete  a  fluid,  and  are  lined  inter- 
nally with  hairs  pointing  downwards.  Up  the  out- 
side of  the  pitcher  there  is  a  line  of  honey  glands 
which  lure  the  insects  to  their  destruction.  Flies 
and  other  insects  which  fall  into  this  pitcher  cannot 
get  out  again  and  are  actually  digested  by  the  plant." ^ 
In  the  example  where  the  idea  of  an  eel-trap  sug- 
gested the  possible  function  of  the  similar  struct- 
ure in  the  plant,  Utricularia,  we  find  one  of  the 
most  striking  illustrations  of  this  mode  of  ana- 
logical inference.  It  was  an  easy  and  natural 
transition  from  similarity  of  structure  to  similarity 
of  function.  To  give  an  idea  of  the  great  number 
of  teleological  phenomena  in  the  vegetable  and 
animal  world,  and  the  wealth  of  possible  sugges- 
tion stored  away  in  these  various  structures,  and 
disclosed  by  a  sagacious  analysis,  I  quote  a  remark 

1  Lubbock,  Scientific  Lectures,  pp.  4,  5. 


ANALOGY  215 

of  Sir  John  Lubbock's  in  commenting  upon  the 
variation  of  color  and  markings  of  caterpillars  :  "  I 
should  produce  an  impression  very  different  from 
that  which  I  wish  to  convey,  were  I  to  lead  you  to 
sup]30se  that  all  these  varieties  have  been  explained 
or  are  understood.  Far  from  it ;  they  still  offer  a 
large  field  for  study ;  nevertheless,  I  venture  to 
think  the  evidence  now  brought  forward,  however 
imperfectly,  is  at  least  sufficient  to  justify  the  con- 
clusion that  there  is  not  a  hair  or  a  line,  not  a  spot 
or  a  color,  for  which  there  is  not  a  reason,  —  which 
has  not  a  purpose  or  a  meaning  in  the  economy  of 
nature."  ^ 

An  illustration  given  by  Darwin  shows  this  mode 
of  inference  applied  to  the  sphere  of  animal  life 
also.  He  says :  "  The  great  size  of  the  bones  of 
the  megatherioid  animals  was  a  complete  puzzle  to 
naturalists  until  Professor  Owen  lately  solved  the 
problem  with  remarkable  ingenuity.  The  teeth 
indicate,  by  their  simple  structure,  that  these  mega- 
therioid animals  lived  on  vegetable  food,  and  prob- 
ably on  the  leaves  and  small  twigs  of  trees ;  their 
ponderous  forms  and  great,  strong,  curved  claws 
see7n  so  little  adapted  for  locomotion  that  some  emi- 
nent naturalists  have  actually  believed  that,  like 
the  sloths,  to  which  they  are  intimately  related, 
they  subsisted  by  climbing  back  downwards  on 
trees,  and  feeding  on  the  leaves.  It  was  a  bold, 
not  to  say  preposterous,  idea,  to  conceive  even  ante- 
diluvian trees  with  branches  strong  enough  to  bear 
animals  as  large  as  elephants.  Professor  Owen, 
1  Lubbock,  Scientific  Lectures,  pp.  66,  67. 


216  INDUCTIVE  LOGIC 

with  far  more  probability,  believes  that,  instead  of 
climbing  on  the  trees,  they  pulled  the  branches 
down  to  them,  and  tore  up  the  smaller  ones  by 
the  roots,  and  so  fed  on  the  leaves.  The  colossal 
breadth  and  weight  of  their  hinder  quarters,  which 
can  hardly  be  imagined  without  having  been  seen, 
become,  on  this  view,  of  obvious  service,  instead  of 
being  an  encumbrance:  their  apparent  clumsiness 
disappears.  With  their  great  tails  and  their  huge 
heels  firmly  fixed  like  a  tripod  on  the  ground,  they 
could  freely  exert  the  full  force  of  their  most 
powerful  arms  and  great  claws.  Strongly  rooted, 
indeed,  must  have  been  that  tree  which  could  have 
resisted  such  force !  The  Mylodon,  moreover,  was 
furnished  with  a  long  extensile  tongue  like  that  of  the 
giraffe,  which,  by  one  of  those  beautiful  provisions 
of  nature,  thus  reaches,  with  the  aid  of  its  long  neck, 
its  leafy  food."  ^  Throughout  we  observe  analogical 
inference  based  upon  these  teleological  marks,  and 
furnishing  a  basis  for  a  satisfactory  hypothesis. 

We  see  what  a  wide  field  thus  opens  in  the 
region  of  biology  alone  for  the  discovery  of  resem- 
blances leading  to  the  appreciation  of  the  fuller 
teleological  significance  of  plant  and  animal  life. 

In  the  illustrations  given,  both  of  the  teleologi- 
cal and  other  forms  of  analogy,  we  notice  that  its 
chief  logical  function  is  that  of  suggestion  of  some 
hypothesis  which  may  or  may  not  be  afterwards 
confirmed  by  subsequent  experiment.  Some  of  the 
most  important  discoveries  of  science  have  arisen 
from  analogical  suggestions.  Sir  John  Herschel 
1  Darwiu,  Voyage  of  a  Naturalist,  pp.  106,  107. 


ANALOGY  217 

was  led  by  observed  analogies  to  predict  certain 
phenomena  afterwards  verified  experimentally  by 
Faraday.  Herschel  had  noticed  that  a  screw-like 
form,  known  as  helicoidal  dissymmetry,  was  ob- 
served in  three  cases,  namely,  in  electrical  helices, 
plagihedral  quartz  crystals  (that  is,  crystals  having 
an  oblique  spiral  arrangement  of  planes),  and  the 
rotation  of  the  plane  of  polarization  of  light.  As 
Herschel  himself  said :  '^  I  reasoned  thus :  Here 
are  three  phenomena  agreeing  in  a  very  strange 
peculiarity.  Probably  this  peculiarity  is  a  connect- 
ing link,  physically  speaking,  among  them.  ISTow, 
in  the  case  of  the  crystals  and  the  light,  this  prob- 
ability has  been  turned  into  certainty  by  my  own 
experiments.  Therefore,  induction  led  me  to  con- 
clude that  a  similar  connection  exists,  and  must 
turn  up,  somehow  or  other,  between  the  electric 
current  and  polarized  light,  and  that  the  plane  of 
polarization  w^ould  be  deflected  by  magneto-elec- 
tricity." Herschel  thus  anticipated  Faraday's  ex- 
perimental discovery  of  the  influence  of  magnetic 
strain  upon  polarized  light.^ 

Another  important  discovery  —  the  germ-theory 
of  epidemic  disease  —  was  first  suggested  by  an 
analogy.  In  the  theory,  as  expressed  by  Kircher, 
and  favored  by  Linnaeus,  and  afterwards  supported 
by  Sir  Henry  Holland,  its  special  strength,  accord- 
ing to  Professor  Tyndall,  "  consisted  in  the  perfect 
parallelism  of  the  phenomena  of  contagious  disease 
with  those  of  life.  As  a  planted  acorn  gives  birth 
to  an  oak  competent  to  produce  a  whole  crop  of 
1  Jevons,  Principles  of  Science,  p.  630. 


218  INDUCTIVE  LOGIC 

acorns,  each  gifted  with  the  power  of  reproducing  the 
parent  tree,  and  as  thus  from  a  single  seedling  a 
whole  forest  may  spring,  so,  it  is  contended,  these 
epidemic  diseases  literally  plant  their  seeds,  grow 
and  shake  abroad  new  germs,  which,  meeting  in  the 
human  body  their  proper  food  and  temperature, 
finally  take  possession  of  whole  populations."  ^ 

The  theory  of  evolution  "was  first  suggested  to 
Mr.  Darwin  by  the  analogous  phenomena  observed 
in  artificial  selection  and  breeding.  The  transition 
to  natural  selection  was  easily  made,  especially  as, 
on  reading  Malthus,  On  Poj) illation,  he  conceived 
the  idea  of  a  struggle  for  existence  as  the  inevitable 
result  of  the  rapid  increase  of  organic  beings.  This 
idea  necessitated  the  natural  selection,  which  he 
needed  to  account  for  results  similar  to  the  artifi- 
cial selection,  and  thus  his  theory  grew  out  of  an 
analogy  as  its  beginning.  Moreover,  in  the  devel- 
opment of  the  theory  in  its  manifold  details,  other 
analogies  proved  also  suggestive.  For  instance, 
there  is  the  supposed  analogy  between  the  growth 
of  a  species  and  the  growth  of  an  individual. 
It  supposes,  for  example,  as  Professor  Clifford  has 
put  it,  "that  the  race  of  crabs  has  gone  through 
much  the  same  sort  of  changes  as  every  crab  goes 
through  now,  in  the  course  of  its  formation  in  the 
egg,  —  changes  represented  by  its  pristine  shape 
utterly  unlike  what  it  afterwards  attains,  and  by 
its  gradual  metamorphosis  and  formation  of  shell 
and  claws."  - 

1  Tyndall,  Fragments  of  Science,  p.  287. 

2  Clifford,  Lectures  and  Essays,  p.  80. 


ANALOGY  219 

The  genii-theory  of  putrefaction,  first  suggested 
by  Schwann,  received  confirmation  through  certain 
resemblances  noted  by  Professor  Lister  between 
fermentation  and  putrefaction.  In  his  Introduc- 
tory Lecture  before  the  University  of  Edinburgh, 
Professor  Lister  called  attention  to  the  fact  that 
fermentation  and  putrefaction  present  a  very 
striking  parallel.  In  each  a  stable  compound  — 
sugar  in  one  case,  albumen  in  the  other  —  under- 
goes extraordinary  chemical  changes  under  the 
influence  of  an  excessively  minute  quantity  of  a 
substance  which,  regarded  chemically,  would  be 
considered  inert.  It  was  pointed  out,  also,  by  Pro- 
fessor Lister,  in  this  connection,  that,  as  was  well 
known,  one  of  the  chief  peculiarities  of  living  or- 
ganisms, is  that  they  possess  extraordinary  powers 
of  effecting  chemical  changes  in  materials  in  their 
vicinity  out  of  all  proportion  to  their  energy  as 
mere  chemical  compounds.  Such  being  the  facts 
in  the  case,  and,  moreover,  the  fermentation  of 
sugar  being  generally  allowed  to  be  occasioned  by 
the  presence  of  living  organisms.  Professor  Lister's 
inference  was  that  putrefaction  was  due  to  an 
analogous  agency.^ 

A  discovery  in  quite  a  different  sphere,  that  of 
mathematics,  leading  to  the  branch  of  analytical 
geometry,  was  first  suggested  to  Descartes  through 
observing  the  resemblances  existing  between  geom- 
etry and  algebra.  In  a  similar  manner,  Boole  was 
led  by  the  resemblances  noted  between  algebra 
and  logic,  to  give  expression  to  the  same  in  a  sys- 
1  Tyndall,  Fragments  of  Science,  pp.  300-302. 


220  INDUCTIVE  LOGIC 

teiii  which  he  called  the  laws  of  thought,  and  which 
has  become  the  basis  of  a  general  or  symbolic  logic. 

While  there  are  thus  unquestionable  evidences  of 
the  value  of  analogy  as  a  form  of  inference,  there 
are  also  cases  of  false  analogy  unfortunately  so  nu- 
merous as  to  discredit  the  process  wholly  in  some 
quarters.  It  will  be  well,  therefore,  to  indicate 
some  of  the  requirements  of  true  analogy  :  — 

1.  In  the  first  place  the  resemblance  must  be  a 
preponderating  one;  that  is,  the  phenomena  com- 
pared must  show  a  more  striking  agreement  than 
difference.  Some  writers  have  balanced  agreement 
against  difference  upon  a  purely  numerical  basis  of 
comparison,  forming  what  may  be  called  an  analogi- 
cal ratio,  with  points  of  similarity  forming  the  numer- 
ator, and  the  points  both  of  similarity  and  difference, 
plus  the  unknown,  that  is,  the  total  number,  form- 
ing the  denominator.  Such  a  representation  of  the 
force  of  an  analogy  is  given  by  Mill,  Bain,  and 
others.  I  think,  however,  that  this  representation 
is  apt  to  be  misleading  in  producing  the  impression 
that  the  mere  number  of  points  of  agreement,  irre- 
spective of  their  significance,  is  the  chief  feature  of 
analogy.  Whereas  it  is  the  weight  of  the  agreeing 
attributes,  and  not  the  number,  that  counts.  As  has 
been  before  said,  in  analogy  we  weigh  instances, 
and  do  not  count  them.  The  analogical  ratio  ex- 
pressed numerically,  as  above,  is  really  equivalent 
to  the  ratio  of  probability  which  will  be  described  in 
the  following  chapter.  I  have  therefore  changed 
the  usual  wording  of  this  requirement,  so  that  it 
reads,  the  resemblances  must  be  more  striking  than 


ANALOGY  221 

the  differences.  This  provides  for  cases  when  per- 
haps a  few  points  of  resemblance  will  be  of  such  a 
nature  as  to  outweigh  many  points  of  difference  in 
the  total  estimate. 

This  requirement  also  excludes  all  fanciful  anal- 
ogies and  all  resemblances  resting  upon  a  figurative 
rather  than  a  real  basis.  For  instance,  the  advo- 
cates of  annual  Parliaments  in  the  time  of  the 
Commonwealth,  urged  their  case  on  the  analogical 
ground  that  a  body  politic  is  similar  to  a  living  body 
and  that  serpents  annually  cast  their  skin,  which, 
being  no  doubt  for  a  beneficial  purpose,  might  well 
be  imitated. 

2.  In  noting  the  points  of  resemblance  between 
two  phenomena,  all  circumstances  which  are  known 
to  be  effects  of  one  cause  must  therefore  be  re- 
garded not  as  many,  but  as  one.  For  instance,  two 
chemical  oxides  may  be  compared;  the  effects  com- 
mon to  each  may  be  due  to  the  presence  of  the 
oxygen  which  each  contains  and  therefore  must  not 
be  regarded  in  the  light  of  independent  marks  of 
similarity. 

3.  If  we  infer  by  analogy  that  a  substance  pos- 
sesses a  certain  property  which  we  know  is  incom- 
patible with  some  one  or  other  known  properties 
of  the  substance,  the  analogy  is  at  once  discredited. 
We  may  infer  that  the  moon  is  inhabited,  by  virtue 
of  the  many  points  of  resemblance  between  the 
moon  and  the  earth.  However,  the  fact  that  the 
moon  has  no  atmosphere  necessary  to  sustain  life, 
at  once  makes  such  an  argument  based  upon  an- 
alogy wholly  out  of  the  question. 


222  INDUCTIVE  LOGIC 

4.  There  are  certain  special  requirements  refer- 
ring to  that  particular  form  of  analogy  which  is 
based  upon  teleological  considerations.  They  are 
as  follows  :  — 

a.  This  principle  must  never  be  used  as  an  argu- 
ment against  an  observed  fact,  or  an  established 
law  of  nature.  While  this  precaution  is  not  neces- 
sary at  the  present  time,  in  scientific  circles  at 
least,  still  there  was  a  time  when  its  counsel  was 
sorely  needed.  When  in  astronomy  it  was  proved 
that  there  were  suns  gravitating  around  other  suns, 
without  our  solar  system,  this  was  objected  to  upon 
the  following  ground,  as  given  by  one  Nicholas 
Fuss,  a  celebrated  astronomer,  at  the  end  of  the 
eighteenth  century  :  "  What  is  the  good  of  some 
luminous  bodies  revolving  round  others  ?  The  sun 
is  the  only  source  whence  the  planets  derive  light 
and  heat.  Were  their  entire  systems  of  suns  con- 
trolled by  other  suns,  their  neighborhood  and  their 
motions  would  be  objectless,  their  rays  useless.  The 
suns  have  no  need  to  borrow  from  strange  bodies 
what  they  themselves  have  received  as  their  own. 
If  the  secondary  stars  are  luminous  bodies,  what  is 
the  end  of  their  motives  ?  " 

There  is,  moreover,  another  abuse  of  the  principle 
of  final  causes,  which  has  also  historic  interest 
rather  than  any  present  pertinence  ;  namely,  oppos- 
ing certain  false  teleological  ideas  to  established 
discoveries  or  inventions,  with  a  mistaken  zeal,  in 
defence  of  a  Divine  Providence.  For  instance,  at 
the  time  of  Jenner's  great  discovery,  an  English 
physician,  Dr.  Eowley,  said  of  small-pox  :  "  It  is  a 


ANALOGY  223 

malady  imposed  by  the  decree  of  heaven,  and  vac- 
cination is  an  audacious  and  sacrilegious  violation 
of  our  holy  religion.  The  designs  of  these  vaccina- 
tors appear  to  defy  heaven  itself,  and  the  very  will 
of  God."  The  introduction  of  winnowing  machines 
into  Scotland  met  Avith  bitter  opposition  on  the 
ground  that  the  winds  were  the  work  of  God,  and 
that  the  wind  thus  artificially  raised  was  a  veritable 
^'devil's  wind,"  as  they  were  wont  to  call  it.  Sir 
Walter  Scott,  in  Old  Mortality,  has  the  old  Mause 
say  to  her  mistress :  "  Your  ladyship  and  the  stew- 
ard are  wishing  Cuddie  to  use  a  new  machine  to 
winnow  the  corn.  This  machine  opposes  the  de- 
signs of  Providence,  by  furnishing  wind  for  your 
special  use,  and  by  human  means,  in  place  of  asking 
it  by  prayer,  and  waiting  with  patience  till  Prov- 
idence itself  sends  it." 

h.  Final  causes  should  never  be  employed  to 
explain  phenomena  which  do  not  exist.  As  M. 
riorens  has  said :  "  We  must  proceed  not  from  final 
causes  to  facts,  but  from  facts  to  final  causes ;  that 
is,  we  should  not  superimpose  final  causes  upon 
phenomena.  We  must  see  them  in  phenomena 
themselves,  and  we  must  not  arbitrarily  project  a 
teleological  idea,  purely  subjective,  ujjon  an  objec- 
tive ground.  Thus  in  ancient  times,  Hippocrates 
is  said  to  '  have  admired  the  skill  with  which  the 
auricles  of  the  heart  have  been  made  to  blow  the 
air  i7ito  the  heart. ^  " 

c.  We  must  distinguish  accidental  from  essential 
marks  of  finality,  and  not  be  led  into  fanciful  or 
far-fetched  analogies.     Voltaire  has  expressed  such 


224  INDUCTIVE  LOGIC 

a  defect  when  in  satire  he  made  that  famous  re- 
mark, "Noses  are  made  in  order  to  bear  spectacles." 

Bernardin  de  Saint-Pierre  says:  "Dogs  are  usu- 
ally of  two  opposite  colors,  the  one  light,  the  other 
dark,  in  order  that  whenever  they  may  be  in  the 
house,  they  may  be  distinguished  from  the  furni- 
ture, with  the  color  of  which  they  might  be  con- 
founded. .  .  .  Wherever  fleas  are  they  jump  on 
white  colors.  This  instinct  has  been  given  them, 
that  we  may  the  more  easily  catch  them."  And 
again  the  same  writer  says :  "  The  melon  has  been 
divided  into  sections  by  nature,  for  family  eating."  ^ 
All  such  grotesque  inferences  will  give  an  idea  of 
how  readily  the  imagination  will  run  riot  if  allowed 
to  remain  uncurbed  by  the  reason. 

5.  Analogy  should  never  be  regarded  as  having 
more  weight  than  that  of  extremely  high  probabil- 
ity, even  in  cases  seemingly  most  conclusive.  Its 
true  function  is  suggestive,  leading  to  hypothesis 
and  experiment,  and  it  needs  this  supplementary 
proof.  It  was  an  inference  based  on  analogy,  for 
instance,  which  suggested  the  probability  that  the 
Binomial  Law,  having  proved  to  be  valid  as  regards 
the  second,  third,  and  fourth  powers,  might  also  be 
extended  to  the  fifth,  and  so  on  to  the  other  powers 
indefinitely.  This  suggestion  offered  no  real  basis, 
however,  upon  which  the  Binomial  Theorem  could 
rest;  it  needed  mathematical  demonstration  to  con- 
firm and  generalize  its  expression  in  the  special 
cases  already  experimentally  tested,  so  as  to  cover 

1  The  illustrations  upon  the  abuse  of  final  causes  I  have  taken 
from  Janet's  admirable  chapter,  —  Chapter  VIII.  of  Appendix. 


ANALOGY  225 

all  possible  exponents,  both  j^ositive  and  negative, 
fractional  and  integral. 

So  also  the  discovery  of  the  circulation  of  the 
blood  was  first  suggested  to  Harvey,  as  has  been 
said,  by  analogical  considerations  upon  observed 
teleological  phenomena.  Harvey,  however,  was  not 
content  with  this  suggestion  merely.  He  was  led 
to  experiment  upon  the  veins  and  arteries  ;  he  tied 
an  artery  and  vein,  and  carefully  observed  the  me- 
chanical effects  upon  the  two  sides  of  the  tied  parts. 
Experiments  of  this  nature,  with  close  observation 
and  study,  were  kept  up  most  diligently,  and  with 
rare  perseverance,  for  nineteen  years,  before  he  had 
traced  the  entire  course  of  the  blood  through  all 
parts  of  the  human  body,  and,  in  a  manner  wholly 
satisfactory  to  himself,  verified  the  first  statement 
of  this  theory. 


CHAPTER   XV 

Probability 

There  are  certain  plienomena  of  such  a  nature 
that  their  antecedents,  being  extremely  complex, 
cannot  be  adequately  comprehended  by  observation, 
however  searching  it  may  be ;  nor  can  they  be  sub- 
jected to  any  analysis  that  will  disclose  the  causal 
elements  to  which  the  effect  in  question  is  due. 
Moreover,  with  seemingly  the  same  antecedents, 
the  event  sometimes  happens,  and  sometimes  does 
not ;  and  even  with  antecedents  associated  with  an 
event  as  cause  and  effect  respectively,  nevertheless 
the  event  does  not  occur  as  we  should  naturally 
expect,  while  with  antecedents  associated  with  the 
contradiction  of  the  event  as  cause  and  effect  re- 
spectively, we  find  the  occurrence  of  the  event  quite 
contrary  to  what  we  should  naturally  expect.  The 
evidence  of  a  constant  connection  between  antece- 
dent and  consequent,  that  we  have  found  in  so  many 
cases  which  we  have  examined,  is  here  wholly  lack- 
ing. Eegularity  has  been  replaced  by  irregularity 
respecting  such  plienomena.  For  instance,  I  throw 
dice  repeatedly ;  the  antecedent  shaking  of  the 
box,  and  tossing  the  dice  upon  the  table,  is  about 
the  same  each  time,  at  least  the  difference  can- 
226 


PROBABILITY  227 

not  be  determined,  and  yet  the  results  vary  with 
each  successive  throw.  The  causal  determination 
in  each  case  is  so  complex  as  to  be  beyond  com- 
putation ;  the  initial  position  of  the  dice,  the  force 
of  their  ejection  from  the  box,  the  height  of  the 
box  above  the  table  when  they  leave  it,  the  ine- 
qualities of  the  table  itself,  a  variation  between 
the  physical  and  geometrical  centres  of  gravity 
of  the  dice,  etc.,  all  these  make  the  antecedent 
so  complex  that  a  slight  variation  in  any  one  of 
these  conditions  will  affect  the  result.  We  find, 
therefore,  double  sixes  at  one  time,  a  three  and 
four  at  another,  and  so  on  indefinitely. 

Or,  again,  it  sometimes  happens  that  with  perfect 
sanitary  conditions  a  contagious  disease  will  appear, 
that  has  always  been  regarded,  and  that  correctly,  as 
due  to  imperfect  sanitation  ;  or,  an  entire  disregard 
of  sanitary  requirements  and  of  all  the  laws  of 
health  may  yet  give  rise  to  no  disease  of  special 
moment.  Certain  conditions  of  temperature,  at- 
mospheric pressure,  velocity  and  direction  of  the 
wind,  may  one  day  bring  storm  and  rain,  and  as 
far  as  observation  can  detect,  similar  conditions 
may  again  bring  fair  weather.  So,  also,  the  rise 
and  fall  in  stock  and  money  markets  is  extremely 
susceptible  to  the  varying  conditions  of  indefi- 
nitely complex  forces  wholly  beyond  all  powers 
of  determination  or  of  prediction.  Such  phe- 
nomena present  a  problem  which  the  methods  of 
inductive  inquiry  cannot  deal  with.  Observation 
is  not  far-reaching  enough  to  provide  the  data  for 
the  solution  of  the  problem,  and,  even  if  it  were. 


228  INDUCTIVE  LOGIC 

our  methods  of  computation  and  determination 
are  not  sufficiently  adequate  to  solve  problems  of 
so  many  terms  and  of  so  complex  a  nature. 

The  experimental  methods  are  designed  to  test 
causes  suggested  by  analogy,  or  a  mental  analysis ; 
but  in  such  phenomena  as  these,  the  problem  is 
not  simply  to  find  a  causal  connection.  The  causal 
connection  may  be  established  beyond  all  reasona- 
ble doubt,  and  yet  the  cause  obtains  in  the  midst 
of  so  complex  a  setting  that  the  problem  is  really 
this, — to  determine  Avhether  a  cause,  whose  exact 
nature  may  be  known  or  unknown,  will  prove 
operative  or  inoperative.  The  cause  may  be  al- 
ways present  and  even  its  exact  nature  may  be 
known,  and  yet  the  complex  circumstances  at- 
tending it  may  be  of  such  a  character  that  one 
alone,  or  two  or  more  combining,  may  neutralize 
the  operation  of  the  cause,  and  on  the  other  hand 
a  slight  variation  of  the  combined  circumstances 
may  promote  and  even  accelerate  the  operation  of 
the  cause  in  question.  The  problem  then  is  to 
determine  how  often  the  event  happens,  and  how 
often  it  fails  of  happening,  the  complex  and  in- 
determinate antecedent  being  present  in  all  the 
instances  examined. 

When  we  begin  to  count  instances,  we  are  re- 
minded that  we  must  be  in  the  near  neighborhood 
of  the  sphere  of  enumerative  induction.  Enumera- 
tive  induction,  it  will  be  remembered,  treats  in- 
stances by  noting  the  number  of  observed  coincident 
happenings  of  the  antecedent  and  consequent  under 
investigation,  no  attempt  being  made   to   analyze 


PROBABILITY  229 

their  respective  contents,  or  to  determine  a  causal 
connection  more  definitely  by  means  of  any  one  or 
more  of  the  inductive  methods  of  research  and  veri- 
fication. The  result  of  such  an  investigation  may 
be  formulated  in  a  proposition  of  the  form,  Every 
A  is  B.  This,  strictly  interpreted,  has  the  force  of, 
Every  A  that  has  been  observed  is  B.  The  enu- 
meration of  the  kind  of  instances  which  we  are  dis- 
cussing in  this  chapter,  however,  differs  from  this 
in  that  the  observation  leads  to  a  twofold  result, 
—  a  set  of  instances  in  which  it  is  observed  that 
the  ^'s  are  B^s  also,  another  set,  however,  in 
which  the  ^'s  are  not  J5's.  These  instances  are 
of  such  a  nature  that  the  observed  A  is  an  ante- 
cedent so  extremely  complex  that  the  element 
within  it,  which  is  a  cause  capable  of  producing 
B,  may  either  be  absent  without  producing  an 
appreciable  change  in  the  general  nature  of  A,  or, 
being  present,  may  be  neutralized  by  some  other 
element  of  ^4  itself.  The  result  gives  a  basis  for  a 
probable  inference  only ;  and  the  nature  of  that  in- 
ference will  depend  upon  the  preponderance  of  the 
observed  happening,  or  of  the  failure  of  the  event 
under  investigation. 

The  probability  attached  to  such  an  inference, 
however,  is  different  from  the  probability  which 
characterizes  the  nature  of  enumerative  induction. 
In  the  latter,  when  the  observation  has  been  widely 
extended  and  no  exceptions  noted,  it  is  usual  to  say 
the  result  expressed  in  the  proposition.  Every  A  is 
B,  has  the  force  of  a  high  degree  of  probability. 
In    the    instances,    however,   whose    investigation 


230  INDUCTRTE  LOGIC 

shows  the  result  that  some  ^I's  are  B^s,  and  some 
not,  and  yet  where  the  former,  for  instance,  far 
outnumber  the  latter  cases,  then  it  may  be  inferred 
that  the  ^I's  which  in  future  we  may  meet  with 
will  probably  be  ^'s ;  and  the  degree  of  probability 
expressed  in  such  a  proposition  is  commensurate 
with  the  preponderance  of  the  number  of  observed 
affirmative  instances  over  the  negative.  Here  the 
probability  refers  to  the  validity  of  an  inference 
concerning  certain  particular  instances,  be  they 
many  or  be  they  few,  which  lie  beyond  the  sphere 
of  our  present  knowledge;  in  enumerative  induc- 
tion, the  probability  is  attached  to  the  universality 
of  the  proposition  affirmed  as  a  result  of  observa- 
tion that  has  not  so  far  detected  an  exception.  In 
the  former  case,  the  question  of  the  universality 
of  the  result  is  conclusively  answered,  and  that  in 
the  negative  ;  there  can  be  no  universal  proposition 
possible,  as  some  instances  give  A  and  B  together, 
others  give  A  with  the  absence  of  B]  and  the 
question  of  probability  that  here  arises,  therefore, 
refers  to  individual  cases  not  yet  examined,  as  to 
whether  they  severally  will  more  likely  correspond 
to  the  set  of  affirmative,  or  to  that  of  the  negative 
instances  already  noted. 

The  comparison  of  the  number  of  happenings 
with  that  of  the  failures  of  an  event  affords  a 
basis  for  three  kinds  of  inference,  all  of  them  in 
the  sphere  of  probability. 

1.  We  find  in  such  a  comparison  a  basis  for  the 
calculation  of  the  probability  of  a  particular  event 
happening,  in  case  there  is  a  repetition  of  the  cir- 


PROBABILITY  231 

cumstances  which,  in  former  cases,  have  sometimes 
produced  the  event,  and  sometimes  have  failed  to 
produce  it.  If,  according  to  former  observation, 
the  event  has  happened,  let  us  say,  seven  times, 
and  failed  three,  the  probability,  expressed  nu- 
merically, of  its  happening  again  is  y-^.  The  rule 
is,  to  express  the  probability  of  an  event,  take  as 
numerator  the  number  of  times  which  the  event 
has  been  observed  to  occur,  and  as  denominator 
the  total  number  observed,  both  of  happening  and 
failure ;  the  fraction  thus  expressed  will  represent 
the  probability  of  the  event  happening.  The  coun- 
ter-probability may  be  represented  by  the  number 
of  observed  failures  of  the  event  divided  by  the 
total  number  of  cases  observed.  The  counter-prob- 
ability, plus  the  probability,  evidently  is  equal  to 
unity.  If,  therefore,  the  probability  is  unity,  the 
counter-probability  will  equal  zero;  that  is,  the 
probability  in  that  case  has  merged  into  certainty. 
Zero,  therefore,  represents  absolute  impossibility. 
All  fractions  between  the  limits  zero  and  one  rep- 
resent varying  degrees  of  probability  from  impos- 
sibility at  one  extreme  to  certainty  at  the  other. 

Not  only  may  there  be  this  inductive  basis  for 
the  calculation  of  probability,  arising  from  actually 
observed  instances ;  there  may  be  also  a  deductive 
calculation  of  probability  based  upon  the  known 
structure  or  nature  of  the  phenomena  themselves 
in  advance  of  any  observation  as  to  their  actual 
behavior.  For  instance,  we  say  the  probability 
of  a  penny  turning  up  heads  is  ^.  Knowing  the 
form  of   the   penny  and   that   there   are   but   two 


232  INDUCTIVE  LOGIC 

possibilities,  heads  or  tails,  and  there  being  no 
reason  why  one  should  more  likely  turn  up  than 
the  other,  we  say  there  is  one  chance  favorable  to 
heads  as  over  against  the  two  chances  which  rep- 
resent the  total  number  of  possibilities  under  the 
existing  circumstances.  With  a  die,  in  the  form 
of  a  perfect  cube,  we  say  there  is  one  chance  of 
its  turning  up  the  face  marked  1,  as  over  against 
the  six  chances  represented  by  the  six  faces,  the 
total  number ;  here  the  probability  is  i  Thus  the 
basis  for  the  calculation  of  probability  may  be  a 
theoretical  as  well  as  an  empirical  one. 

In  the  estimate  of  the  probability  of  an  event  in 
the  actual  conduct  of  affairs,  we  seldom  express 
that  probability  numerically.  I  would  say  that  we 
express  a  degree  of  probability  adverbially  rather 
than  numerically ;  that  is,  we  say  an  event  is  quite 
probable,  or  it  is  very  probable,  or  it  is  extremely 
probable.  The  fact  is  that,  as  regards  most  phenom- 
ena, we  do  not  keep  an  exact  or  even  approximate 
memorandum  of  the  number  of  happenings  compared 
with  that  of  the  failures.  We  rather  classify  our 
observations  in  terms  of  more  or  less.  For  instance, 
certain  circumstances  we  observe  produce  about  as 
many  failures  as  happenings  of  an  event;  other 
circumstances  produce  far  more  happenings  than 
failures ;  others  far  less,  and  so  on.  Consequently 
we  receive  certain  psychological  impressions  of 
varying  degrees  of  intensity  according  to  the  pre- 
ponderance of  happening  over  failure,  or  vice  versa; 
this  impression  becomes  the  basis  for  estimating 
the  probability  in  question,  and  the  degree  of  that 


PROBABILITY  233 

probability  is  commensurate  with  the  intensity  of 
the  original  psychological  impression  arising  from 
concepts  of  more  or  of  less.  In  such  a  sphere,  how- 
ever, as  that  devoted  to  the  interests  of  betting, 
gambling,  pool-selling,  book-making,  etc.,  probabili- 
ties are  estimated  according  to  observations  and 
theoretical  considerations,  whose  conditions  are  ex- 
pressed numerically  ;  and  the  amount  risked  in 
each  case  is  strictly  estimated  according  to  the 
exact  ratio  of  probability  to  counter-probability 
under  the  existing  circumstances. 

The  estimation  of  probability  in  terms  of  a 
greater  or  less  degree  is,  however,  more  usual,  and 
applicable  to  the  conduct  of  human  life  generally. 
It  has  special  force  and  utility  as  a  mode  of  infer- 
ence, when  the  observed  instances  so  far  outnumber 
the  exceptions  as  to  create  an  impression  of  such 
a  high  degree  of  probability  as  to  approximate 
practical  if  not  theoretical  certainty.  For  instance, 
it  has  been  noted  over  a  wide  field  of  observation, 
that  a  second  attack  of  scarlet  fever  is  extremely 
rare.  Exceptions  have  occurred  and,  therefore,  by 
enumerative  induction  it  is  impossible  to  general- 
ize the  universal  proposition  that  a  second  attack 
will  never  occur.  It  is,  however,  possible  to  assert 
with  somewhat  positive  assurance  that  it  is  highly 
probable  that  a  person  will  be  exempt  from  a  second 
attack. 

Or,  you  hear  that  a  person,  whose  name  is  un- 
known to  you,  has  met  with  an  accident  in  the 
city  of  New  York,  resulting  fatally.  You  are  not 
alarmed,  and  perhaps  the  possibility  does  not  even 


234  INDUCTIVE  LOGIC 

suggest  itself  to  you,  that  the  unknown  person  may 
prove  to  be  a  member  of  your  own  family,  or  a 
friend  who  at  the  time  is  known  to  be  in  New 
York.  The  probability  against  such  a  suggestion 
is  so  large  as  to  preclude  even  the  thought  of  it. 
Suppose,  however,  the  accident  occurred  at  one  of 
the  suburban  stations.  Your  knowledge  that  your 
friend  rides  on  one  of  the  suburban  trains  each  day 
to  and  from  town,  may  be  the  ground  of  some 
anxiety,  because  in  this  case  the  range  of  possibili- 
ties is  materially  narrowed.  Suppose,  moreover, 
that  the  station  where  the  accident  occurred  is  at 
the  village  where  your  friend  resides,  your  anxiety 
receives  an  additional  increment;  and,  again,  sup- 
pose it  is  at  the  hour  at  which  your  friend  ordi- 
narily reaches  this  station,  there  is  then  increased 
apprehension  on  his  account.  Thus,  as  further 
knowledge  limits  the  number  of  total  possible  cases, 
the  denominator  of  the  probability  fraction  is  contin- 
ually decreasing,  and  therefore  the  probability  itself 
continually  increases,  until  it  has  developed  from  a 
fraction  of  insignificant  proportions  to  one  which  is 
suggestive  of  great  anxiety  and  susx^ense. 

2.  The  comparison  of  failure  and  happening  of 
events  based  upon  observation,  or  theoretical  con- 
siderations of  structure  and  nature,  leads  also  to 
inferences  concerning  large  numbers  of  instances 
considered  together.  If  a  memorandum  is  kept  of 
the  number  of  times  an  event  has  happened,  and 
the  number  of  times  it  has  failed,  and  the  total 
number  of  instances  examined  be  sufficiently  great, 
then  the  resulting  ratio  of   favorable  instances  to 


PROBABILITY  235 

the  total  number  will  be  found  approximately 
repeated,  if  a  second  set  of  an  equal  number  of 
instances  be  likewise  examined.  There  is  a  law  of 
tendency  whereby  nature  seems  to  repeat  herself 
even  when  the  attendant  circumstances  of  an  event 
are  most  complex,  and  beyond  all  powers  of  accu- 
rate determination.  As  the  result  of  observations 
extending  over  thousands  and  thousands  of  in- 
stances, it  is  affirmed  that  about  one-fourth  of  the 
children  born  in  the  world  die  before  the  age  of  six 
years,  and  about  one-half  before  the  age  of  sixteen. 
Take  a  group  of  ten  children,  the  ratios  would  per- 
haps be  deviated  from  very  materially ;  in  a  group 
of  a  hundred  the  deviation  is  apt  to  be  less ;  in  a 
group  of  a  thousand,  still  less ;  and  in  a  group  of 
one  hundred  thousand,  the  ratios  as  above  given 
would  be  substantially  realized.  The  approxima- 
tion would  be  so  near  that  the  error  would  be  insig- 
nificant as  compared  with  total  number  of  cases. 
The  following  law,  therefore,  expresses  this  ten- 
dency, —  that  while  in  a  small  number  of  instances 
there  is  irregularity  in  the  observed  ratio  between 
the  number  of  times  a  given  event  has  happened 
and  its  failures,  still  in  a  large  number  of  instances 
this  ratio  tends  towards  a  constant  limit.  This  is 
clearly  seen  in  the  pitching  of  a  penny ;  10  throws 
might  very  possibly  result  in  7  heads  and  3  tails ; 
in  100  throws,  however,  the  ratio  expressing  the 
result  as  to  heads  and  tails  observed  will  be  much 
nearer  i  than  in  the  former  case ;  while  if  1000  or 
10,000  throws  be  observed,  the  result  will  approxi- 
mate the  ratio  ^.     The  comparison  of  observed  cases 


236  INDUCTIVE  LOGIC 

with  the  number  given  by  the  calculation  of  the 
probabilities  in  question  has  been  made  by  Quetelet, 
also  by  Jevons.  Their  results  are  most  significant 
and  interesting.  Quetelet  made  4096  drawings 
from  an  urn  containing  20  black  balls  and  20  white. 
Theoretically,  he  should  have  drawn  as  many  white 
as  black  balls,  204:8  each;  the  actual  drawings  re- 
sulted in  2066  white  balls  and  2030  black.  Jevons 
made  20,480  throws  of  a  penny ;  the  theoretical 
result  should  have  been  10,240  heads;  the  actual 
result  was  10,353  heads. 

The  tendency  towards  a  constant  ratio  in  aggre- 
gates containing  a  considerable  number  of  instances 
is  strikingly  illustrated  in  the  record  of  baptisms 
taken  from  an  old  parish  register  in  England.  The 
number  of  male  baptisms  registered  to  every  1000 
female  ran  as  follows  for  the  respective  years  from 
1821  to  1830 :  1048,  1047,  1047,  1041,  1049,  1046, 
1047, 1043, 1043, 1034.  We  see  with  what  surprising 
accuracy  the  constant  ratio  was  repeated  substan- 
tially, year  after  year.  This  tendency  to  approximate 
a  constant  ratio  is  seen  even  in  such  indeterminate 
events  as  railroad  accidents.  Here  the  causes  pro- 
ducing the  accidents  are  so  numerous,  so  diverse,  so 
complex  and  extending  over  so  large  an  area,  as, 
for  example,  the  whole  of  the  United  States,  that 
we  should  think  that  the  results  would  exhibit  so 
many  variations  from  any  definite  ratio  as  abso- 
lutely to  elude  all  attempts  at  accurate  determina- 
tion. The  following  figures,  however,  given  by  the 
Interstate  Commerce  Commission,  indicate  results 
wonderfully  corresponding  for  year  after  year :  — 


PROBABILITY 


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PROBABILITY  239 

An  examination  of  these  figures  will  disclose  the 
fact  that  there  is  a  striking  approximation  to  an 
accurately  proportionate  distribution  of  the  number 
of  accidents,  of  the  killed  and  of  the  injured, 
throughout  these  several  years.  It  will  be  noticed, 
also,  that  the  distribution  among  employes,  passen- 
gers, other  persons,  etc.,  tends  towards  a  regularity 
that  is  remarkable  when  we  consider  the  extreme 
complexity  of  the  circumstances  that  must  combine 
to  produce  these  results.  A  like  regularity  seems 
to  pervade  every  department  of  life.  The  total 
number  of  crimes  is  approximately  the  same,  year 
after  year;  the  annual  death-rate,  the  apportion- 
ment of  deaths,  moreover,  to  the  several  diseases  as 
their  evident  causes,  the  number  of  missent  letters 
that  reach  the  Dead-Letter  Office  at  Washington 
each  year,  the  annual  number  of  suicides,  of  di- 
vorces, all  these  diverse  events  indicate  a  regularity, 
in  the  long  run,  as  regards  their  numerical  estimate. 

The  results  which  are  thus  attained  regarding  ag- 
gregates cannot  be  stated  as  probable  results.  If  a 
sufficiently  large  number  of  instances  are  taken,  the 
result  will  be  certain  within  a  very  small,  and  in 
many  cases  an  insignificant  margin.  In  estimating 
the  probability  of  a  single  event,  the  question  is 
whether  it  will  happen  or  not  happen,  and  the  ele- 
ment of  uncertainty  is  therefore  prominent.  In 
dealing  with  aggregates,  however,  no  such  element 
of  uncertainty  enters ;  the  question  is  not  whether 
or  not  there  will  be  certain  results,  the  question 
concerns  rather  the  degree  of  exactness  with  which 
the  results  will  approximate  a  definite  ratio.     And 


240  INDUCTIVE  LOGIC 

the  law  of  tendency  is,  that  the  larger  the  number 
of  instances,  the  greater  will  be  the  approximation 
to  an  accurate  and  definite  result. 

This  is  especially  illustrated  in  the  numerous  in- 
surance companies,  whose  business  is  conducted  upon 
the  basis  of  an  approximately  constant  death-rate. 
For  instance,  the  general  procedure  is  somewhat  as 
follows  :  Suppose  10,000  persons  insure  their  lives  at 
$1000  per  individual,  and  the  annual  death-rate  ob- 
served over  a  rude  extent  of  territory,  and  including 
a  very  large  number  of  instances,  amounts  to  200 
persons  out  of  10,000.  The  losses  then  to  the  in- 
surance company  will  amount  annually  to  $200,000 
on  such  a  basis.  These  losses,  distributed  among 
the  10,000  insuring  in  the  company,  would  amount 
to  $20  apiece.  The  company,  therefore,  has  a 
numerical  basis  for  calculating  the  amount  which 
each  person  must  pay  in  order  to  cover  the  annual 
losses,  and  provide  an  assured  revenue  for  the  com- 
pany. 

I  have,  of  course,  stated  the  problem  in  round 
numbers,  merely  to  illustrate  in  general  the  princi- 
ple involved ;  the  actual  calculation  is  more  compli- 
cated, because,  in  each  particular  case,  the  age  of  the 
individual  and  the  varying  death-rates  for  different 
years  must  be  taken  into  account.  The  substantial 
standing  of  the  innumerable  insurance  companies 
in  our  country  bears  witness  to  the  fact  that  these 
enterprises  are  based  upon  a  practical  certainty  re- 
garding death-rates  when  applied  to  large  aggre- 
gates. Chance  is  thus  eliminated  almost  entirely; 
that  which  would  be  a  serious  risk  as  regards  an  in- 


PROBABILITY  241 

dividual  is  substantially  void  of  all  risk  when  large 
numbers  are  concerned. 

Moreover,  statistics  covering  different  classes  are 
often  most  valuable  in  indicating  tendencies  opera- 
tive in  the  classes  when  compared  one  with  another. 
According  to  M.  Loua  (Economiste  Frcmgais,  1882, 
Vol.  I.  p.  179),  the  following  are  the  figures  of  the 
annual  mortality  in  Paris  :  — 

The  rich  and  well-to-do  classes,   156  out  of  every  10,000 

inhabitants. 
The  poor,  285  out  of  every  10,000  inhabitants. 

So  also,  in  England,  the  average  duration  of  life 
among  the  wealthy  classes  is  from  55  to  56  years ; 
for  the  working  classes  it  falls  to  28  years,  or  even 
lower. ^  Such  comparisons  are  significant  in  indi- 
cating underlying  forces  in  society  that  otherwise 
might  be  overlooked,  or,  at  least,  not  adequately 
appreciated,  and  which  a  limited  observation  could 
not  accurately  reveal.  Mr.  Darwin,  after  observing 
and  experimenting  upon  a  very  large  number  of 
plants,  found  the  following  figures  respecting  the 
relative  productivity  of  cross  and  spontaneously 
self -fertilized  flowers :  As  regards  the  number  of 
seeds  per  pod  yielded  by  cross  and  self-fertilized 
flowers,  the  ratio  was  100  to  41  respectively ;  the 
crossed  seeds  compared  with  an  equal  number  of 
the  spontaneously  self-fertilized  seeds  were  heavier, 
in  the  ratio  of  100  to  88.^  The  ratios  thus  disclosed 
in  examining  a  large  number  of  instances  could 
not  have  been  gained  by  any  experimental  method 

1  Gide,  Political  Economy,  p.  405. 

2  Darwin,  Ct^oss  and  Self  Fertilization,  p.  165. 

R 


242  iNDUCTm:  logic 

adapted  for  dealing  with  individual  instances.  Al- 
though the  cause  is  not  quantitatively  determined, 
a  tendency  of  a  constant  nature  towards  a  definite 
end  is  clearly  indicated. 

Eace  characteristics  are  often  disclosed  by  com- 
parative statistics,  and  the  presence  or  absence  of 
moral  causes  especially  are  thus  revealed  which 
otherwise  could  not  be  determined  with  any  con- 
siderable degree  of  definiteness.  The  following 
tables  will  indicate  this  :  — 

Suicides.  —  In  European  cities  the  number  of 
suicides  per  100,000  inhabitants  is  as  follows : 
Paris,  42;  Lyons,  29;  St.  Petersburg,  7;  Moscow, 
11;  Berlin,  36;  Vienna,  28;  London,  23;  Eome, 
8;  Milan,  6*;  Madrid,  3;  Genoa,  31;  Brussels,  15; 
Amsterdam,  14 ;  Lisbon,  2  ;  Christiania,  25  ;  Stock- 
holm, 27  ;  Constantinople,  12 ;  Geneva,  11 ;  Dres- 
den, 51.  Madrid  and  Lisbon  show  the  lowest, 
Dresden  the  highest  figure. 

The  average  annual  suicide  rate  in  countries  of 
the  world  per  100,000  persons  living  is  given  by 
Barker  as  follows :  Saxony,  31.1  ;  Denmark,  25.8 ; 
Schleswig-Holstein,  24.0;  Austria,  21.2;  Switzer- 
land, 20.2;  France,  15.7;  German  Empire,  14.3; 
Hanover,  14.0;  Queensland,  13.5;  Prussia,  13.3; 
Victoria,  11.5 ;  New  South  Wales,  9.3 ;  Bavaria,  9.1 ; 
New  Zealand,  9.0;  South  Australia,  8.9;  Sweden, 
8.1;  Norway,  7.5;  Belgium,  6.9;  England  and 
Wales,  6.9;  Tasmania,  5.3;  Hungary,  5.2;  Scot- 
land, 4.0;  Italy,  3.7;  Netherlands,  3.6;  United 
States,  3.5  ;  Russia,  2.9  ;  Ireland,  1.7  ;  Spain,  1.4. 


PROBABILITY  243 

The  causes  of  suicide  in  European  countries  are 
reported  as  follows  :  Of  100  suicides  :  Madness,  de- 
lirium, 18  per  cent ;  alcoholism,  11 ;  vice,  crime,  19 ; 
different  diseases,  2  ;  moral  sufferings,  6 ;  family 
matters,  4 ;  poverty,  want,  4 ;  loss  of  intellect,  14 ; 
consequence  of  crimes,  3 ;  unknown  reasons,  19. 

Homiddes.  —  Italy  takes  the  lead  of  European 
nations,  with  an  average  annual  crop  of  murders  of 
2470,  a  ratio  per  10,000  deaths  of  29.4 ;  Spain  fol- 
lows, with  a  ratio  of  23.8,  and  1200  murders ;  Aus- 
tria, ratio  of  8.8,  and  600  murders ;  France,  ratio  of 
8.0,  and  662  murders;  England,  ratio  of  7.1,  and 
377  murders.  The  figures,  however,  represent 
actual  murders,  not  homicides  from  all  causes,  as 
do  those  in  the  United  States  table. 

Illegitimacy.  —  Of  each  1000  births,  the  number 
illegitimate,  according  to  statistics  published  in 
London,  1892,  were  :  Kussia,  27  ;  Ireland,  28 ;  Hol- 
land, 33  ;  England  and  Wales,  46;  Switzerland,  47; 
Italy,  73  ;  Norway,  74 ;  Scotland,  79 ;  Prussia,  80 ; 
France,  84 ;  Hungary,  85  ;  Belgium,  88 ;  Denmark, 
93;  Sweden,  101;  Saxony,  125;  Bavaria,  141;  Aus- 
tria, 147.  No  accurate  statistics  for  the  United 
States  exist.  The  lowest  rate  in  Europe  is  that 
of  Connaught,  in  Western  Ireland,  7  per  1000. — 
Dr.  Albert  Leffingwell,  Summit,  N.J. 

3.  When  phenomena  indicate  a  marked  departure 
from  the  ratio  of  frequency  as  determined  by  prior 
observation,  or  by  theoretical  considerations,  then 
it  is  ordinarily  inferred  that  a  new  cause  has  be- 
,come  operative,  not  before  existent,  or,  if  present, 


244  INDUCTIVE   LOGIC 

its  effect  neutralized.  For  instance,  we  would  natu- 
rally expect  a  die  to  show  the  face  three,  on  an 
average,  about  once  in  six  throws.  But  if  it  re- 
peatedly turns  up  three  in  succession,  and  no  other 
number  appears,  or  appears  but  rarely,  we  are 
warranted  in  inferring  that  the  die  is  loaded. 
The  number  of  homicides  in  the  United  States  in 
189-4:  far  exceeded  the  annual  number  observed  for 
the  several  years  preceding.  This  discrepancy  is 
easily  accounted  for  by  the  fact  that  the  natural 
number  was  swollen  by  the  deaths  caused  by  the 
strikers  and  rioters  in  the  month  of  July  of  that 
year.  So  also  a  marked  departure  from  the  annual 
death-rate  of  such  a  city  as  jS'ew  York  is  at  once 
an  urgent  suggestion  to  the  Board  of  Health  to 
start  investigations  that  will  unearth  the  hidden 
cause  that  one  is  constrained  to  believe  must  be 
present.  Such  causes  as  defective  drains,  preva- 
lence of  epidemics,  etc.,  are  again  and  again  found 
to  accompany  an  increase  of  the  average  death-rate. 
Under  such  circumstances,  the  method  of  investi- 
gation, when  practicable,  which  should  be  pursued, 
is  to  endeavor  to  break  up  the  total  into  smaller 
groups  of  a  specific  nature.  Thus,  if  the  death-rate 
for  the  year  is  appreciably  increased,  examine  the 
death-rate  per  month.  See  if  any  month  shows  a 
marked  departure  from  the  average.  If  so,  this 
will  suggest  a  careful  investigation  of  the  circum- 
stances and  characteristics  of  the  month  in  question. 
Or  it  may  be  possible  to  make  a  geographical  dis- 
tribution of  the  total  over  different  sections  of  the 
city  under  investigation.    Some  special  locality  may 


PROBABILITY  245 

indicate  an  unusually  large  death-rate.  Investiga- 
tion, therefore,  at  that  point  may  reveal  a  lurking 
cause  of  disease,  otherwise  unnoticed. 

By  similar  considerations  also,  it  is  often  possible 
to  distinguish  between  a  chance  coincidence,  and  a 
determinate  cause  which  has  produced  the  event  in 
question.  For,  if  the  possibility  of  some  one  defi- 
nite cause  is  considered  out  of  the  question,  and 
the  origin  of  the  event  is  found  among  complex 
phenomena  of  such  a  number  and  variety  that  they 
may  form  an  indefinite  number  of  combinations, 
only  one  of  which  can  possibly  produce  the  event 
in  question,  then  the  probability  that  the  event  has 
actually  been  produced  by  such  a  chance  combina- 
tion is  extremely  small.  We  are  then  thrown  back 
upon  the  other  hypothesis,  that,  instead  of  one  out 
of  many  possible  combinations,  there  is  some  one 
determinate  cause  operative  in  the  case.  Its  nature 
may  not  be  definitely  indicated,  but  at  least  the 
possibility  of  its  presence  is  suggested. 

This  line  of  reasoning  is  illustrated  in  the  fol- 
lowing account  of  the  discovery  of  the  existence  of 
iron  in  the  sun,  in  the  researches  of  Bunsen  and 
Kirchhoff :  ^'  On  comparing  the  spectra  of  sunlight 
and  of  the  light  proceeding  from  the  incandescent 
vapor  of  iron,  it  became  apparent  that  at  least  sixty 
bright  lines  in  the  spectrum  of  iron  coincided  with 
dark  lines  in  the  sun's  spectrum.  Such  coinci- 
dences could  never  be  observed  with  certainty, 
because,  even  if  the  lines  only  closely  approached, 
the  instrumental  imperfections  of  the  spectroscope 
would  make  them  apparently  coincident,  and  if  one 


246  INDUCTIVE  LOGIC 

line  came  within  half  a  millimetre  of  another,  on 
the  map  of  the  spectra,  they  could  not  be  pro- 
nounced distinct.  Now  the  average  distance  of  the 
solar  lines  on  Kirchhoff's  map  is  two  millimetres, 
and  if  we  throw  down  a  line,  as  it  were  by  pure 
chance,  on  such  a  map,  the  probability  is  about  ^ 
that  the  new  line  will  fall  within  one-half  milli- 
metre on  one  side  or  the  other  of  some  one  of  the 
solar  lines.  To  put  it  in  another  way,  we  may 
suppose  that  each  solar  line,  either  on  account  of 
its  real  breadth,  or  the  defects  of  the  instrument, 
possesses  a  breadth  of  one-half  millimetre,  and  that 
each  line  in  the  iron  spectrum  has  a  like  breadth. 
The  probability,  then,  is  just  i  that  the  centre  of 
each  iron  line  will  come  by  chance  within  one  milli- 
metre of  the  centre  of  a  solar  line,  so  as  to  appear 
to  coincide  with  it.  The  probability  of  casual  coin- 
cidence of  each  iron  line  with  a  solar  line  is  in  like 
manner  i.  Coincidence  in  the  case  of  each  of  the 
sixty  iron  lines  is  a  very  unlikely  event  if  it  arises 
casually,  for  it  would  have  a  probability  of  only 
(i)  *^  or  less  than  one  in  a  trillion.  The  odds,  in 
short,  are  more  than  a  million  million  millions  to 
unity  against  such  a  casual  coincidence.  But  on 
the  other  hypothesis,  that  iron  exists  in  the  sun,  it 
is  highly  probable  that  such  coincidences  would  be 
observed ;  it  is  immensely  more  i)robable  that  sixty 
coincidences  would  be  observed  if  iron  existed  in 
the  sun,  than  that  they  should  arise  from  chance. 
Hence,  by  our  principle,  it  is  immensely  probable 
that  iron  does  exist  in  the  sun."  ^ 

1  Jevons,  Principles  of  Science,  pp.  24-4,  245. 


PROBABILITY  247 

This  princi]Dle  is  also  illustrated  in  instances  of 
circumstantial  evidence.  In  such  cases,  the  observed 
combination  of  so  many  diverse  circumstances,  even 
as  regards  an  indefinite  number  of  minor  details, 
precludes  the  hypothesis  of  casual  coincidence,  and 
suggests  some  one  definite  cause  that  will  prove  a 
unifying  principle  of  explanation  of  all  the  attend- 
ant circumstances.  As  Mr.  Justice  Bullen  says : 
"  A  presumption  Avhich  necessarily  arises  from  cir- 
cumstances is  very  often  more  convincing  and 
more  satisfactory  than  any  other  kind  of  evidence. 
It  is  not  within  the  reach  and  compass  of  human 
abilities  to  invent  a  train  of  circumstances  which 
shall  be  so  connected  together  as  to  amount  to  a 
proof  of  guilt  without  affording  opportunities  to 
contradict  a  great  part,  if  not  all,  of  these  circum- 
stances." 

The  following  account,  taken  from  The  New  York 
Laiv  Journal,  illustrates  the  probative  force  of  cir- 
cumstantial evidence :  — 

In  Nicholas  v.  Commonwealth  (March  1895,  21  S,  E.  K. 
364)  the  Supreme  Court  of  Appeals  of  Virginia  sustained  a 
conviction  of  murder,  the  criminal  agency  being  established 
by  circumstantial  evidence.  The  following  extract  from  the 
opinion  presents  the  main  facts  which  implicated  the  de- 
fendant :  — 

"  On  the  8th  day  of  December,  1892,  Philip  Norman 
Nicholas,  the  plaintiff  in  error,  one  James  Mills,  and  his 
wife,  Anna  A.  Mills,  and  their  three  small  children,  were 
living  in  the  upper  part  of  Henrico  County,  on  a  farm 
known  as  the  '  Wickham  Place,'  about  one  mile  from  James 
Kiver.  Nicholas  was  the  renter  of  this  farm,  and  cultivated 
it  on  shares.     He  was  himself,  however,  chiefly  engaged  as 


248  INDUCTIVE  LOGIC 

a  trapper,  having  a  number  of  traps  set  along  both  sides  of 
the  river.  He  employed  James  Mills,  with  whom  he  lived, 
and  one  William  Judson  Wilkerson,  as  subtenants,  to  do 
the  farm  work,  for  a  j^ortion  of  his  share  of  the  crops. 
Wilkerson  lived  with  an  aged  mother  in  a  small  house  very- 
near  to  Mills'  house  —  near  enough  to  see  into  the  windows 
of  one  house  from  the  other.  Philip  N.  Nicholas,  the  pris- 
oner, was  an  unmarried  man,  and  lived  in  a  room  of  the 
house  occupied  by  James  Mills  and  his  family.  The  evi- 
dence shows  that  on  the  night  before  the  drowning,  the 
prisoner,  James  Mills,  and  William  J.  Wilkerson  were 
together  at  the  house  of  Mrs.  Wilkerson,  the  latter's 
mother,  and  there  arranged  and  determined  upon  a  trip 
across  the  river  the  next  morning,  to  take  a  bee  tree.  This 
expedition  was  suggested,  planned,  and  carried  out  by  the 
prisoner.  Wilkerson  was  very  unwilling  to  go,  and  finally 
consented  at  the  suggestion  of  his  mother,  who  said  that,  as 
Mr.  Nicholas  seemed  so  anxious  for  him  to  go,  he  had  better 
do  so.  Mills  was  unwilling  to  go  unless  Wilkerson  went. 
Wilkerson  said  he  would  rather  plough  than  go.  The  prisoner 
replied,  '  If  you  will  go,  you  shall  not  lose  anything.'  In  the 
course  of  conversation  which  resulted  in  this  expedition 
being  agreed  upon,  both  Mills  and  Wilkerson  stated,  in  the 
presence  of  Nicholas,  that  they  could  not  swim,  and  were 
very  much  afraid  of  water ;  that  they  did  not  like  water 
more  than  knee-deep.  The  fact  that  they  could  not  swim 
was  generally  known  to  their  friends.  It  is  further  shown 
that  it  was  the  habit  of  Nicholas  to  go  every  morning,  early, 
to  the  river,  to  examine  his  traps.  And  it  appears  from  the 
evidence  that  on  the  morning  of  the  day  the  drowning 
occurred  he  went  to  the  river  about  daylight,  and  returned 
about  breakfast  time,  and,  when  questioned  about  it,  said: 
'I  did  not  go  to  my  traps  this  morning.  I  was  sick.'  He 
afterwards  told  Mrs.  Wilkerson  he  did  not  catch  anything. 
Everything  being  in  readiness  to  carry  out  the  plan  for  the 
day,  these  three  men  started  from  home  about  nine  o'clock 
in  the  morning,  equipped  with  everything  necessary  for 


PROBABILITY  249 

taking  the  bee  tree  ;  having  with  them  two  buckets  holding 
two  and  one-half  to  three  gallons  each  for  the  honey,  two 
axes,  one  hatchet,  and  a  piece  of  netting  to  protect  the  per- 
son from  the  bees.  The  boat  used  belonged  to  one  Joseph 
Bruin,  and  on  their  way  to  the  river  an  uncle  of  the  owner 
was  asked  if  they  might  use  the  boat,  and  was  told  they 
could  get  the  key  which  unlocked  the  boat  from  its  fastening 
to  the  bank  from  Bruin,  the  owner.  The  prisoner  replied 
that  he  had  a  key  of  his  own,  and  had  often  used  it  before 
without  permission.  It  appears  that  they  landed  on  the 
Chesterfield  side  of  the  river,  at  a  point  one  mile  and  a  half 
from  where  any  one  lived,  and  proceeded  to  the  bee  tree, 
which  was  one  mile  from  the  point  of  landing.  Investiga- 
tion showed  that  there  were  no  tracks  about  the  point  of 
landing  but  those  of  the  three  men  going  from  and  returning 
to  the  boat.  It  further  appears  from  the  statement  of  the 
prisoner  that  after  reaching  the  tree  they  concluded  not  to 
cut  it,  because  it  was  a  large  tree,  near  the  main  road,  and 
might  get  them  into  trouble,  and  for  the  further  reason  that 
the  hole  was  small,  and  it  might  not  have  any  honey  in  it 
anyhow.  The  tree  was  afterwards  cut  by  order  of  the  Magis- 
trate and  found  to  be  full  of  honey.  It  further  appears  that 
the  boat  was  a  small  one,  about  ten  feet  long  and  about  two 
and  one-half  feet  wide,  and  that  both  in  going  over  and 
returning  the  prisoner  sat  in  the  extreme  rear  of  the  boat, 
with  his  face  to  the  front,  and  that  Wilkerson  and  Mills  sat 
in  front  of  him,  with  their  faces  to  the  front  and  their  backs 
to  the  accused.  This  position  of  the  parties  the  prisoner 
admitted  very  reluctantly,  when  questioned  about  it.  When 
returning,  and  about  fifty  yards  from  the  Henrico  shore, 
the  boat  suddenly  filled  with  water,  and  Mills  and  Wilker- 
son were  drowned,  and  the  prisoner  swam  to  shore.  The 
next  day  the  Magistrate  of  the  district  was  notified  of  the 
occurrence,  and  an  investigation  was  set  on  foot.  The  boat 
was  gotten  out  of  the  water,  and  it  was  found  that  immedi- 
ately under  the  seat  where  Nicholas  sat  there  were  three 
holes,  freshly  bored  with  an  inch  and  a  half  auger.    The 


250  INDUCTIVE  LOGIC 

evidence  of  the  owner  of  the  boat  shows  that  on  Tuesday 
evening,  the  Cth  of  December,  he  used  his  boat,  and  it  was 
sound.  It  was  taken  by  Nicholas  for  this  fatal  trip  Thurs- 
day morning,  the  8th  of  December.  Further  investigation 
discovered  fresh  pine  shavings  corresponding  to  size  of  the 
holes  and  to  the  wood  the  boat  was  made  of,  which  had 
been  thrown  into  the  water,  but  had  drifted  upon  the  shore 
near  the  point  where  the  boat  had  stood  fastened  to  the 
Henrico  side.  There  were  also  found  corn-cobs  which  had 
been  cut  to  exactly  fit  the  holes  in  the  boat,  which  had  also 
drifted  to  the  same  point.  It  was  shown  that  the  prisoner 
had  in  his  possession  an  auger  just  the  size  of  the  holes. 
This  the  prisoner  at  first  denied,  but  afterwards  said  that  it 
must  be  about  the  place  somewhere.  Diligent  search  was 
made  for  the  auger,  but  it  was  never  found. 

"  Taken  together,  the  case  is  an  interesting  illustration  of 
the  conclusive  probative  force  of  circumstantial  evidence, 
provided  there  is  enough  of  it.  The  old  saying  that  '  mur- 
der will  out '  is  almost  unexceptionally  true  as  to  murders 
of  elaborate  stealth  and  complexity  of  detail.  Once  let  a 
clue  be  obtained  to  the  chain  of  causation  and  motive,  and 
the  mystery  unravels  almost  of  itself.  It  is  quite  natural 
that  most  of  the  elaborately  planned  murders  of  recent 
times  should  have  been  by  poison.  And  the  Harris,  Buch- 
anan and  Meyer  cases  in  New  York  disclose  how  compara- 
tively easy  detection  and  conviction  are  in  crimes  of  such 
class.  It  is  significant  that  two  of  the  greatest  enigmas  in 
American  criminal  annals  during  the  last  quarter  of  a  cen- 
tury have  been  the  Nathan  murder  and  the  Borden  murder. 
In  both  cases  the  killing  was  done  not  by  methods  calcu- 
lated to  conceal  the  agency  of  a  murderer,  but  in  the  most 
primitive  and  brutal  manner.  No  traceable  physical  clue 
to  any  particular  person  was  left,  and  we  are  inclined  to 
believe  that  in  both  cases  the  connection  of  the  murderer 
with  the  crime  was  merely  casual  or  accidental."  ^ 

1  The  New  York  Law  Journal,  Tluirsday,  May  2,  1895. 


PROBABILITY  251 

In  the  various  illustrations  which  have  been  given 
we  find  that  the  theory  of  probability  provides  a 
method  of  dealing  with  phenomena  which  cannot 
be  subjected  to  the  ordinary  inductive  methods. 
The  phenomena  are  so  complex  that  a  specific  cause 
cannot  be  determined,  for  the  real  cause  in  question 
is  a  correlation  of  many  diverse  forces,  and  if  only 
a  few  instances  are  examined  no  causal  connection 
will  be  disclosed ;  it  is  necessary,  therefore,  to  deal 
with  large  numbers,  statistical  averages,  etc.,  in 
order  to  detect  an  emerging  relation  of  a  causal 
character,  expressed  by  a  constant  ratio.  This  ratio 
once  determined,  it  becomes  a  further  test,  as  we 
have  already  seen,  when  the  results  widely  depart 
from  it,  to  suggest  the  presence  of  a  new  force  out- 
side of  the  combinations  to  which  the  effect  would 
be  naturally  referred  according  to  the  indications  of 
the  probability-ratio.  This  latter  mode  of  inference 
is  akin  to  the  method  of  residues,  for  the  inference 
in  question  is  based  upon  the  fact  that  the  probabil- 
ity-ratio Avill  account  for  only  a  certain  frequency 
of  occurrence  of  the  event  under  investigation;  a 
marked  excess  must  be  accounted  for  by  positing  a 
definitely  operative  cause.  And  if  an  antecedent 
of  such  a  nature  is  known  to  be  present,  the  sugges- 
tion at  once  rises  in  our  thought  that  this  in  all 
probability  is  the  cause  producing  this  excess  in  the 
results. 


CHAPTEK   XVI 

Empirical  Laws 

There  is  a  class  of  laws  wliich  are  intermediate 
between  a  universal,  inductively  grounded  by  scien- 
tific determination,  and  a  law  of  tendency  wliicli  is 
the  expression  of  the  probability  of  the  happening 
of  an  event  in  spite  of  recognized  exceptions.  These 
are  laws  which  have  been  observed  to  obtain  under 
given  conditions  of  time,  place,  and  circumstance, 
and  yet  the  causal  relation  not  sufficiently  deter- 
mined to  warrant  a  necessary  extension  of  the 
same  to  a  sx)here  beyond  that  Avherein  it  has  been 
observed  to  be  operative.  Such  laws  are  known  as 
Empirical  Laws.  We  have,  therefore,  three  classes 
of  laws  of  varying  degrees  of  probability.  The 
first  is  where  there  has  been  a  scientifically  deter- 
mined causal  connection  between  antecedent  and 
consequent ;  and  not  only  have  no  exceptions  been 
noted,  but  the  possibility  of  there  being  an  excep- 
tion has  been  eliminated  by  strict  experimental 
methods.  The  second  is  where  the  regularity  of 
sequence  has  been  broken  by  actual  exceptions,  and 
the  result  of  the  observations  of  instances  gives  an 
indication  only  of  the  relative  frequency  of  occur- 
rence and  failure  which  will  probably  characterize 
252 


EMPIRICAL  LAWS  253 

other  events  of  that  nature.  The  third  class  and, 
as  has  been  said,  an  intermediate  class,  comprises 
all  expressions  of  uniform  sequence  or  coexistence, 
where  no  exception  whatsoever  has  been  noted,  and 
yet  there  is  no  ground  for  necessitating  a  universal 
expression  of  the  observed  uniformity.  There  is 
here  always  a  possibility  of  an  exception  appearing, 
or  of  an  exception  having  been  overlooked.  This 
produces  an  element  of  uncertainty  which  pervades 
all  phenomena  of  this  sort. 

There  are  several  kinds  of  empirical  laws,  as 
follows :  — 

1.  Where  the  causal  relation  is  in  process  of 
scientific  determination;  a  uniform  connection 
between  phenomena  has  been  observed,  and  as 
yet  has  not  been  proved.  All  laws,  finally  deter- 
mined as  expressions  of  causal  connection,  pass 
through  this  empirical  stage.  Some  expressions 
of  uniform  relations  never  pass  beyond  this  stage, 
because,  as  we  have  seen,  the  nature  of  the  phenom- 
ena may  be  such  as  to  preclude  all  experiment  or 
even  indirect  verification. 

Empirical  laws  may  become  ultimate  laws  or 
derivative  laws,  as  the  case  may  be.  Ultimate 
laws  are  those  wherein  the  causal  relation  between 
a  simple  antecedent  and  its  corresponding  conse- 
quent has  been  scientifically  determined  in  terms 
of  their  exact  quantitative  variation,  and  expressed 
in  the  simplest  form  possible.  The  derivative 
laws,  however,  as  the  name  indicates,  are  more 
concrete  expressions  of  the  ultimate  and  simpler 
laws  to  which  they  are  referred  as  special  cases. 


254  INDUCTIVE  LOGIC 

An  empirical  law  may  be  proved  directly  an  ulti- 
mate law,  or  be  proved  a  derivative  law  directly 
traceable  to  an  ultimate  law,  as  its  basis,  or  logical 
ground.  We  may  observe  that  a  glass  of  ice-water 
always  shows  drops  of  moisture  on  its  outer  sur- 
face. This  uniformity  as  thus  expressed  has  the 
force  only  of  an  empirical  law.  No  attempt  hav- 
ing been  made,  as  yet,  to  explain  the  presence 
of  the  moisture,  its  empirical  nature  is  evident. 
But  as  soon  as  the  moisture  on  the  glass  is  traced 
to  the  condensation  of  the  moisture  in  the  atmos- 
phere owing  to  the  difference  of  temperature  be- 
tween the  atmosphere  and  the  cold  surface  of  the 
glass,  we  have  the  empirical  law  becoming  a  deriva- 
tive law;  that  is,  the  expression  of  a  uniform 
sequence  directly  traceable  to  the  more  ultimate 
law  of  the  saturation  and  condensation  of  vapors. 
The  progress  of  scientific  and  logically  accurate 
thought  is  always  marked,  therefore,  by  the  resolu- 
tion of  empirical  generalities  into  derivative  and 
ultimate  laws. 

2.  The  character  of  an  empirical  law  is  attached 
to  the  relation  existing  between  antecedent  and 
consequent,  when  that  relation  is  a  complex  one  in 
which  a  simple  causal  relation  is  so  involved  with 
other  elements  entering  into  combination  with  it, 
that  its  real  nature  is  thus  hidden  and  cannot  read- 
ily be  disclosed.  This  class  includes  all  causal  rela- 
tions due  to  collocations  of  various  kinds  that  are 
necessary  to  produce  the  required  effect.  As  Mill 
has  pointed  out :  "  It  is  the  nature  of  an  empirical 
law  that  we  do  not  know  whether  it  results  from 


EMPIRICAL  LAWS  255 

the  different  effects  of  one  cause  or  the  effects  of 
different  causes.  We  cannot  tell  whether  it  depends 
wholly  upon  laws,  or  partly  upon  laws  and  partly 
upon  a  collocation.  If  it  depends  upon  a  colloca- 
tion, it  will  be  true  in  all  the  cases  in  which  that 
particular  collocation  exists.  But  since  we  are 
entirely  ignorant,  in  case  of  its  depending  upon  a 
collocation,  what  the  collocation  is,  we  are  not  safe 
in  extending  the  law  beyond  the  limits  of  time  and  ^ 
place  in  which  we  have  actual  experience  of  its 
truth.  Knowing  of  no  rule  or  principle  to  which 
the  collocations  themselves  conform,  we  cannot 
conclude  that  because  a  collocation  is  proved  to 
exist  within  certain  limits  of  place  or  time,  it  will 
exist  beyond  those  limits."  ^ 

There  are  many  illustrations  of  such  observed 
generalities  Avhere  the  effect  is  due  largely,  if  not 
altogether,  to  collocations.  The  effect  of  certain 
medicines  upon  the  human  system,  the  opening  and 
shutting  of  some  flowers  at  certain  hours  of  the 
day,  the  local  action  of  tides  at  various  places  on 
the  earth's  surface,  the  adaptation  of  certain  plants 
to  a  peculiar  kind  of  soil,  the  reappearance  of  some 
chronic  diseases,  as  hay-fever,  at  the  same  season 
each  year,  even  to  the  very  day  of  the  month,  all 
such  generalities  have  merely  an  empirical  weight, 
and  the  effects  mentioned  are  largely  due  to  collo- 
cations that  cannot  be  definitely  determined.  So 
also  certain  laws  or  customs  may  have  proved 
beneficial  in  the  countries  in  which  they  have  been 
tried,  and  yet,  in   countries  where   condition   and 

1  Mill,  Logic,  Book  III.  Chapter  XVI.  §  4. 


256  INDUCTIVE  LOGIC 

circumstance  are  radically  different,  they  may  fail 
wholly  of  beneficial  results.  There  may  be  also 
certain  industrial  circumstances  which  in  one  coun- 
try might  be  conducive  to  prosperity,  and  in  an- 
other country  to  adversity.  Certain  agricultural 
methods  which  in  one  section  of  the  country  tend 
to  an  increase  of  productive  power,  in  another 
might  prove  a  complete  failure.  A  governmental 
policy  may  in  one  country  lead  to  unparalleled  suc- 
cess ;  in  another,  however,  a  like  policy  might  lead 
to  disastrous  results. 

The  famous  formula  of  Malthus,  that  population 
tends  to  increase  in  a  geometrical  progression,  whilst 
the  means  of  subsistence  can  only  increase  in  an 
arithmetical  progression,  can  have  only  an  empirical 
force.  Its  extension  into  an  indefinite  future  is 
unwarrantable.  As  is  known,  production  has  in- 
creased enormously  and  at  a  ratio  vastly  greater 
than  any  contemplated  by  Malthus  as  at  all  in  the 
range  of  possibility.  Many  causes,  on  the  other 
hand,  may  combine  to  check  the  rapid  increase  of 
population.  The  collocations  here  are  so  complex 
as  to  defy  any  definite  prediction.  This  is  true  of 
all  tendencies  which  are  due  to  present  social  con- 
ditions ;  the  conditions  themselves  may  so  vary  in 
time  to  come  as  to  change  totally  the  accepted 
generalizations  of  to-day.  Their  empirical  character 
is,  therefore,  most  evident. 

3.  A  third  class  of  empirical  laws  comprises  all 
those  generalizations  which  represent  an  aggregate 
of  properties  in  the  same  individual.  In  all  such 
cases  no  causal   relation   has  been  specifically  de- 


EMPIRICAL  LAWS  257 

termined  between  the  properties  themselves,  or 
between  the  properties  and  the  whole  in  which  they 
coinhere.  Outside  of  our  experience,  the  proper- 
ties observed  might  be  materially  changed,  and  yet 
not  affect  the  integrity  of  the  concept  in  general. 
A  proposition  such  as  all  swans  are  white  can  have 
only  empirical  force;  for  beyond  our  experience, 
the  discovery  of  black  swans  would  forbid  the  prop- 
osition being  regarded  in  the  light  of  a  universal. 
Many  properties  of  substances  are  thus  referred  to 
the  nature  of  the  substance  itself  as  their  ground, 
and  yet  because  the  exact  causal  relation  is  not  de- 
termined the  connection  can  be  considered  only  as 
an  empirical  one.  In  other  words,  reference  to  some 
ground  as  explanation  of  a  phenomenon,  without 
explaining  why  or  how  such  reference  is  made,  has 
always  the  force  of  an  empirical  law  only.  The  fol- 
owing  are  empirical  generalizations  of  this  nature. 
Copper  is  ductile ;  steel  is  elastic ;  glass  is  brittle  and 
transparent ;  the  compound  silicates  of  alkalies  and 
alkaline  metals  are  transparent ;  and  other  instances 
of  like  nature  that  can  be  multiplied  indefinitely. 

In  the  sphere  of  biology,  Mr.  Spencer  has  drawn 
attention  to  the  fact  that  "  during  the  era  in  which 
uniformity  of  many  quite  simple  inorganic  rela- 
tions was  still  unrecognized,  certain  organic  rela- 
tions, intrinsically  very  complex  and  special,  were 
generalized.  The  constant  coexistence  of  feathers 
and  a  beak,  of  four  legs  with  an  internal  bony 
framework,  are  facts  which  were,  and  are,  familiar 
to  every  savage.  Did  a  savage  find  a  bird  with 
teeth,  or  a  mammal  clothed  with  feathers,  he  would 


258  INDUCTIVE  LOGIC 

be  as  much  surprised  as  an  instructed  naturalist. 
Now  these  uniformities  of  organic  structure,  thus 
early  perceived,  are  of  exactly  the  same  kind  as 
those  more  numerous  ones  later  established  by 
biology.  The  constant  coexistence  of  mammary 
glands  with  two  occipital  condyles  to  the  skull, 
of  vertebrffi  with  teeth  lodged  in  sockets,  of  frontal 
horns  with  the  habit  of  rumination,  are  generaliza- 
tions as  purely  empirical  as  those  known  to  the 
original  hunter.  The  botanist  cannot  in  the  least 
understand  the  complex  relation  between  papilio- 
naceous flowers  and  seeds  borne  in  flattened  pods ; 
he  knows  these  and  like  connections  simply  in  the 
same  way  that  the  barbarian  knows  the  connections 
between  particular  leaves  and  particular  kinds  of 
wood."  ^  Such  knowledge  as  Mr.  Spencer  here  de- 
scribes is  a  knowledge  of  the  coexistence  of  two 
phenomena  in  their  totality  which  resist  all  at- 
tempts to  analyze  into  their  component  parts. 
Moreover,  laws  which  are  but  general  descriptions 
of  correlated  events  have  the  same  force  as  the 
descriptions  of  coinhering  attributes  of  substances. 
They,  too,  rank  as  empirical  generalizations.  The 
successive  stages  in  the  growth  of  a  plant  from 
seed  to  flower  and  fruit,  the  embryonic  as  well  as 
the  post-natal  developments  in  animal  life,  the 
habits  and  instincts  of  animals,  —  all  these  are  de- 
scriptive generalizations  without  any  attempt  at 
causal  determination. 

4.  All  generalizations  expressed  in  terms  of  prob- 
ability only,  because  of  known  exceptions,  rank  as 

1  Spencer,  Classification  of  the  Sciences,  p.  .53. 


EMPIRICAL  LAWS  259 

empirical  laws.  Here,  even  in  the  time,  place,  and 
circumstance  of  observation,  the  law  has  not  been 
found  always  valid.  The  significance  of  an  empiri- 
cal law,  if  we  allow  this  latter  class  to  be  included 
under  them,  is  evidently  that  of  the  contradictory 
of  a  law  which  is  the  result  of  a  causal  determi- 
nation. Every  generalization  not  causally  deter- 
mined is  then  to  be  regarded  as  an  empirical  law. 
There  is,  however,  a  narrower  usage  of  the  term 
which  does  not  include  this  latter  class ;  namely, 
a  restriction  of  the  term  empirical  law  to  signify 
the  expression  of  a  relation  which  has  been  found 
constant  throughout  the  sphere  of  •  observation,  and 
yet  where  there  exists  no  known  causal  ground  by 
reason  of  which  we  would  be  warranted  in  infer- 
ring the  continuation  of  this  relation  in  a  sphere 
beyond  that  already  observed.  We  might  add  that 
with  this  there  is  also  the  expectation,  greater  or 
less,  according  to  the  circumstances  attending  the 
phenomena,  that  the  generalized  experience  will 
be  further  confirmed  by  subsequent  observation  in 
a  wider  sphere.  This  restricted  meaning  of  an  em- 
pirical law  is  the  one  generally  understood,  unless 
it  is  implied  to  the  contrary. 

An  empirical  uniformity  generally  results  from 
the  method  of  agreement.  Observed  instances, 
even  so  selected  as  to  vary  the  antecedents  as 
much  as  possible,  cannot  alone  establish  a  law 
of  uniformity  that  shall  have  universal  validity. 
The  method  of  agreement,  we  have  seen,  needed  to 
be  supplemented  by  the  method  of  difference  if 
possible,  or   by   an    hypothesis   capable   of   subse- 


260  INDUCTIVE  LOGIC 

quent  verification.  An  empirical  law  is,  therefore, 
due  either  to  some  deficiency  in  method,  or  to  the 
natural  limitations  of  our  knowledge. 

The  element  of  uncertainty  attached  to  all  infer- 
ences depending  upon  the  extension  of  an  empirical 
law  into  unknown  territory,  it  has  been  insisted 
upon  in  several  quarters,  may  apply  equally  as  well 
to  all  inferences  depending  upon  the  results  of  the 
inductive  methods  even  Avhen  most  scientifically 
determined.  It  is  contended  that  even  a  causal 
relation,  however  firmly  grounded,  and  however 
simple  may  be  its  nature,  nevertheless  presents  an 
empirical  character.  It  may  give  assurances  of  a 
high  degree  of  probability,  but  can  never  produce 
absolute  certitude  in  our  minds.  Mr.  A'enn,  for  in- 
stance, has  styled  his  work  on  induction  Empirical 
Logic,  that  by  the  title  he  might  indicate  his  point 
of  view  in  this  regard.  He  says  in  the  preface  to 
his  work  :  "  By  the  introduction  of  the  term  empir- 
ical into  the  title,  I  wish  to  emphasize  my  belief 
that  no  ultimate  objective  certainty,  such  as  Mill, 
for  instance,  seemed  to  attribute  to  the  resiilts  of 
induction,  is  attainable  by  any  exercise  of  the  hu- 
man reason."  Eegarded  in  this  light,  all  laws  are 
empirical. 

The  distinction,  however,  between  empirical  laws 
in  the  sense  generally  understood,  and  laws  ex- 
pressing causal  relations  scientifically  determined, 
is  a  real  distinction,  and  a  significant  one  as  well. 
And  this  must  not  be  overlooked;  and  it  cannot 
be  obliterated  by  any  shifting  of  the  point  of 
view.     For,  to  doubt  the  validity  of  an  empirical 


EMPIRICAL  LAWS  261 

law  when  extended  to  a  sphere  beyond  that  which 
has  been  observed,  casts  a  reflection  merely  up- 
on one's  ability  adequately  to  determine  the  con- 
nections existing  between  the  various  elements 
involved  in  the  particular  phenomena  under  in- 
vestigation. This  is,  however,  no  confession  of 
inability  to  discover  the  causal  connections  of 
phenomena  in  general,  in  such  a  manner  as  to 
determine  laws  of  universal  validity.  To  say  that 
all  laws  have  only  empirical  significance  is  to  re- 
flect upon  the  basal  postulates  of  knowledge.  Our 
world  is  the  world  as  we  know  it,  the  world  of  our 
consciousness.  To  discredit  the  uniformities  and 
regularities  therein  existing,  and  which  find  ex- 
pression in  universal  laws,  is  to  discredit  that 
which  we  feel  obliged  to  think  in  order  that  our 
world  of  knowledge,  regarded  as  a  system,  may 
remain  consistent  with  itself,  that  is,  part  to  part, 
and  part  to  whole.  We  must,  therefore,  regard 
an  empirical  law  not  as  the  final  form  of  knowl- 
edge, or  the  goal  of  inductive  research,  but  rather 
as  marking  a  transition  stage  towards  complete 
causal  determination.  And  even  when,  owing  to 
the  nature  of  certain  phenomena,  we  are  not  able 
to  pass  beyond  this  transition  stage  of  empirical 
determination,  nevertheless,  such  instances  by  con- 
trast bear  unimpeachable  testimony  to  the  fact 
that  there  are  other  phenomena  of  such  a  nature 
that  it  is  possible  to  subject  them  to  an  analysis 
which  will  disclose  causal  connections  of  such  a 
character  as  to  form  a  basis  for  the  formulation  of 
universal  laws. 


CHAPTEK   XVII 

Fallacies 

A  coNsiDERATiox  of  the  various  kinds  of  induc- 
tive fallacies,  and  their  characteristic  features,  may 
be  regarded  as  the  obverse  representation  of  the 
general  theory  of  induction.  From  the  one  point 
of  view  we  consider  the  positive  conditions  of  true 
inductive  inference  ;  from  the  obverse  point  of  view 
we  regard  the  various  breaches  of  these  inductive 
conditions.  The  discussion  of  fallacies,  therefore, 
indicates  no  progress  in  the  elucidation  of  the  sub- 
ject under  consideration ;  it  rather  serves  to  empha- 
size distinctions  and  requirements  already  indicated 
by  presenting  them  in  a  new  light  and  from  a  dif- 
ferent angle.  The  subject  of  fallacies  is  generally 
treated  by  exhibiting  through  various  illustrations 
the  cases  in  which  the  positive  conditions  of  induc- 
tive inference  have  failed  of  satisfactory  fulfilment. 
Such  illustrations  of  the  infringement  of  the  require- 
ments of  valid  induction,  I  have  endeavored  to 
incorporate  in  the  body  of  the  text  in  connection 
with  the  exposition  of  the  various  conditions  and 
requirements  themselves.  In  this  chapter  I  shall 
attempt  to  indicate  those  fallacies  especially  which 
are  due  to  the  psychological  disturbance  of  our 
262 


FALLACIES  263 

normal  logical  processes.  An  enumeration  of  these 
tendencies,  partly  psychological  and  partly  logical, 
may  serve  to  impress  npon  us  the  danger  of  falling 
into  easy  errors,  to  which  the  human  mind  generally 
is  liable.  These  errors  emerge  in  the  various  mental 
processes.     They  are  as  follows  :  — 

I.   Errors  of  Perception. 
II.   Errors  of  Judgment. 

III.  Errors  of  the  Imagination. 

IV.  Errors  of  the  Conceptual  Processes. 

I.  Errors  of  Perception.  —  Observation  is  the  in- 
strument of  research  pre-eminently,  in  all  inductive 
inquiry.  Experiment  is  but  a  method  for  increased 
facility  and  accuracy  of  observation.  We  may  say, 
therefore,  that  all  the  data  of  inductive  inference 
are  furnished  by  this  one  process,  observation.  Any 
derangement  of  our  powers  of  observation  will  affect 
the  nature  of  the  data,  and  therefore  the  nature  of 
the  results  of  induction.  It  becomes,  therefore,  all 
important  that  we  should  be  appraised  at  least  of 
the  various  circumstances  whose  tendency  is  to 
operate  in  the  midst  of  the  perceptive  processes  as 
disturbing  forces.  We  have  the  following  possibili- 
ties of  error  in  the  sphere  of  perception :  — 

1.  Errors  due  to  a  failure  to  take  in  the  whole 
field  of  vision.  There  may  be  portions  omitted 
which  possess  a  determining  significance  as  regards 
the  object  of  investigation.  Thus  exceptions  may 
be  overlooked  that  might  have  an  important  bearing 
upon  some  received  hypothesis ;  or  a  fact  might  be 
passed  by  which,  if  known,  would  prove  highly  sug- 


264  INDUCTIVE  LOGIC 

gestive.  Various  devices  liave  been  employed  to 
enlarge  the  sphere  of  observation  beyond  the  natu- 
ral limits  of  the  senses.  As,  for  instance,  sounds 
which  are  inaudible  to  us  may  be  detected  by  means 
of  a  sensitive  flame ;  the  telescope,  the  microscope, 
serve  to  render  the  distant  near,  and  the  small 
large.  It  had  been  noted  that  there  was  a  sudden 
elongation  of  an  iron  wire  at  a  particular  tempera- 
ture Avhilst  under  longitudinal  strain  during  the  act 
of  cooling  from  a  red  heat ;  an  additional  circum- 
stance was  noted  by  Professor  Barrett  when  per- 
forming the  experiment  in  a  darkened  room,  namely, 
that  at  the  moment  of  elongation  the  wire  suddenly 
evolved  heat,  and  exhibited  a  visible  and  conspicu- 
ous momentary  glow  of  redness.^  This  circum- 
stance it  would  be  impossible  to  note  unless  in  a 
darkened  room.  Thus,  a  prominent  characteristic 
of  scientific  observation  is  the  endeavor  to  extend 
continually  the  sphere  of  observation.  Here  also 
much  depends  upon  the  mental  habit.  There  are 
some  who  naturally  see  wider  and  farther  than 
others.  And  it  is  absolutely  necessary  that  the 
true  observer  should  cultivate  mth  all  assiduity 
such  a  habit  when  it  is  not  a  natural  possession. 
There  is  a  slovenliness  in  observation  which  gives 
to  the  inferences  based  upon  its  results  a  color  of 
indefiniteness  and  inaccuracy,  and  which  proves  a 
fertile  source  of  error. 

It  also  often  happens,  that,  owing  to  the  mind 
being  prepossessed  by  a  certain  idea  or  theory,  re- 
search will  be  thereby  restricted  to  a  limited  region, 
1  Gore,  The  Art  of  Scientific  Discovery ,  p.  321. 


FALLACIES  26o 

and  neighboring  regions  be  wholly  overlooked. 
An  open-eyed  vision,  in  spite  of  all  preconceptions 
or  prejudices,  is  the  prime  requisite  for  securing 
from  all  quarters  the  greatest  possible  array  of 
facts  that  may  in  any  way  tend  to  the  formation 
of  a  clearer  and  more  adequate  judgment. 

2.  A  second  error  of  observation  arises  from  an 
opposite  mental  habit,  a  failure  properly  to  concen- 
trate the  attention  upon  the  relevant  facts  and  so 
to  discriminate  as  to  exclude  from  consciousness,  for 
the  time  being  at  least,  all  irrelevant  details.  The 
lack  of  such  a  discriminating  faculty  leads  either 
to  error,  or  to  the  dearth  of  all  significant  results. 
It  is  necessary  to  avoid  either  extreme,  so  that  there 
may  be  a  sweeping  survey  of  all  the  possible  facts 
relevant  to  the  subject  under  investigation,  com- 
bined at  the  same  time  with  a  concentration  of 
attention  that  is  the  prerequisite  of  a  deep  insight 
into  the  inner  connections  and  interrelations  of 
these  facts.  There  must  be  a  depth  as  well  as  a 
wideness  of  vision. 

There  are  also  errors  arising  from  a  failure  to 
note  significant  differences  in  phenomena  that 
present  striking  surface  resemblances.  Here  the 
closest  scrutiny  is  necessary.  The  older  chemists 
could  not  distinguish  potash  from  soda ;  baryta  and 
strontia  were  formerly  confounded  together,  so  also 
potash  and  csesia.  Throughout  the  whole  realm  of 
scientific  research,  it  should  be  ever  kept  promi- 
nently in  mind  that  surface  differences  may  hide 
essential  resemblances,  and  that  surface  resem- 
blances may  hide  essential  differences. 


266  INDUCTIVE   LOGIC 

3.  Errors  may  arise  from  apperceptive  projection. 
Here  the  objective  elements  of  perception  combine 
with  the  subjective,  so  that  the  complete  perception 
may  contain  elements  which  do  not  correspond  with 
reality.  The  mind  thus  projects  upon  the  field  of 
vision  its  own  coloring.  We  see  often  that  which 
we  wish  to  see,  and  fail  to  see  that  which  we  do  not 
wish  to  see.  When  palladium  was  originally  made 
known  to  the  public,  Chenevix  proceeded  to  examine 
it,  prepossessed  with  the  idea  that  it  was  an  alloy  of 
some  two  known  metals.  This  idea  was  so  projected 
upon  his  experiments,  that  he  at  last  came  to  the 
conclusion  that  it  was  a  compound  of  platinum  and 
mercury.  Chenevix  was  led  into  an  error  of  obser- 
vation, as  was  afterwards  proved  by  Dr.  Wollaston, 
who  himself  had  obtained  palladium  from  the  solu- 
tion of  crude  platina  in  aqua  regia.^  This  error  of 
observation  was  due  to  the  fact  that  he  approached 
the  experiments  with  a  fixed  idea  in  his  mind  as  to 
what  they  should  prove ;  and  being  determined  to 
see  evidences  of  this  in  the  phenomena,  he  uncon- 
sciously read  into  them  that  which  was  not  really 
there. 

II.  Errors  of  Judgment.  —  These  errors  occur  in 
the  interpretation  of  the  data  of  perception.  For 
that  which  is  observed  must  be  referred  to  its 
appropriate  place  in  the  body  of  knowledge  re- 
garded as  a  system,  in  which,  part  must  fit  to  part, 
and  part  to  whole.  Inaccurate  reference  results  in 
manifest  imperfections  and  incongruities  in  that 
part  of  the  system  of  knowledge  to  which  the  ref- 
1  Gore,  The  Art  of  Scientific  Discovery. 


FALLACIES  267 

erence  has  been  made.  And  the  inferences  based 
thereupon  are  naturally  affected  by  this  funda- 
mental error  of  judgment.  These  errors  are  as 
follows :  — 

1.  Errors  due  to  false  associations.  Here,  where 
artificial  or  superficial  associations  are  interpreted 
as  though  they  were  real  causal  connections,  the 
mistake  may  prove  most  serious.  The  most  fertile 
source  of  such  fallacies  is  the  Avrong  interpretation 
of  space  and  time  associations,  regarding  mere  con- 
tiguity in  space  and  time  as  evidence  of  causal 
connection.  Under  this  head  may  be  classed  the 
fallacies,  no7i  causa  pro  causa,  and  _posi  hoc  ergo 
propter  hoc.  Prosperity,  for  instance,  following  the 
enactment  of  certain  industrial  or  tariff  measures, 
is  often  attributed  as  the  effect  of  the  same,  merely 
because  they  appear  in  striking  sequence.  How- 
ever, it  may  be  that  the  prosperity  has  followed  in 
spite  of  the  laws  and  not  on  account  of  them. 

2.  Errors  of  judgment  due  to  emotional  pertur- 
bations. When  the  intellect  is  defiected  from  its 
true  pointing  by  passion,  or  prejudice,  or  super- 
stition, or  any  strong  emotion,  the  consequent 
judgment  is  the  resultant  of  two  forces,  rather 
than  the  expression  of  one.  As  Bacon  says:  "The 
human  understanding  resembles  not  a  dry  light,  but 
admits  a  tincture  of  the  will,  and  passions  which 
generate  their  own  systems  accordingly ;  for  man 
always  believes  more  readily  that  which  he  prefers ; 
his  feelings  imbue  and  corrupt  his  understanding  in 
innumerable  and  sometimes  imperceptible  ways."  ^ 
1  Bacon,  Novum  Organon,  Book  I.  Aphorism  XLIX. 


268  INDUCTIVE  LOGIC 

The  necessity  of  judging  in  a  "dry  light,"  as  far 
as  possible,  is  especially  emphasized  in  the  ethical 
positions  of  Adam  Smith,  and  later  of  Mr.  Sidgwick. 
Adam  Smith  contends  that  one's  duty  must  be 
estimated  from  the  standpoint  of  an  impartial 
spectator  and  critic.  That  is,  man  must,  as  it 
were,  step  out  of  himself,  leaving  feeling  behind, 
and  judge  of  himself  and  of  his  duty  from  a 
purely  objective  point  of  view.  So  also  Mr.  Sidg- 
wick sa3^s  that  one  of  the  chief  difficulties  in  the 
utilitarian  position,  namely,  the  discrepancy  be- 
tween the  egoistic  and  altruistic  claims  upon 
our  activities,  cannot  be  harmonized  satisfactorily, 
when  stated  as  a  problein  of  mere  feeling.  Here 
again  man  must  eliminate  feeling  and  judge  of 
himself  merely  as  one  among  many,  where  each 
counts  for  one  and  no  one  for  more  than  one.  In 
the  light  of  pure  reason  he  may  be  able  to  see 
that  the  good  of  all  is  his  highest  good.  But 
when  that  dry  light  is  colored  by  feeling,  such 
judgment  is  impossible. 

Faraday,  in  his  Observations  on  Mental  Education^ 
has  borne  testimony  directly  to  the  necessity  of 
eliminating  feeling  from  our  judgments.  He  says : 
"The  tendency  to  deceive  ourselves  regarding  all 
we  wish  for  should  be  kept  in  mind,  and  the  neces- 
sity also  of  resistance  to  these  desires.  The  force 
of  the  temptation  which  urges  us  to  seek  for  such 
evidence  and  appearances  as  are  in  favor  of  our 
desires,  and  to  disregard  those  which  oppose  them, 
is  wonderfully  great.  In  this  respect  we  are  all 
more   or   less   active   promoters  of  error.      I   will 


FALLACIES  269 

simply  express  my  strong  belief  that  that  j)oint  of 
self-education  which  consists  in  teaching  the  mind 
to  resist  its  desires  and  inclinations  until  they  are 
proved  to  be  right,  is  the  most  important  of  all, 
not  only  in  things  of  natural  philosophy,  but  in 
every  department  of  daily  life."  ^ 

3.  Errors  of  judgment  due  to  the  common  frail- 
ties of  human  nature.  Such  errors  Bacon  has  styled 
"Idols."  His  enumeration  is  not  only  complete, 
but  is  classic  in  its  way,  and  therefore  I  quote  it  at 
this  place  :  "  Four  species  of  idols  beset  the  human 
mind,  to  which,  for  distinction's  sake,  we  have  as- 
signed names,  calling  the  first  Idols  of  the  Tribe, 
the  second  Idols  of  the  Den,  the  third  Idols  of  the 
Market,  the  fourth  Idols  of  the  Theatre. 

"The  formation  of  notions  and  axioms  on  the 
foundation  of  true  induction  is  the  only  fitting 
remedy  by  which  we  can  ward  off  and  expel  these 
idols.  It  is,  however,  of  great  service  to  point  them 
out ;  for  the  doctrine  of  idols  bears  the  same  rela- 
tion to  the  interpretation  of  nature  as  that  of  the 
confutation  of  sophisms  does  to  common  logic.  The 
idols  of  the  tribe  are  inherent  in  human  nature,  and 
the  very  tribe  or  race  of  man ;  for  man's  sense  is 
falsely  asserted  to  be  the  standard  of  things;  on 
the  contrary,  all  the  perceptions,  both  of  the  senses 
and  the  mind,  bear  reference  to  man  and  not  to  the 
universe,  and  the  human  mind  is  like  those  uneven 
mirrors  which  impart  their  own  properties  to  dif- 
ferent objects  from  which  rays  are  emitted,  and 
distort  and  disfigure  them. 

1  Gladstone,  Michael  Faraday,  p.  128. 


270  INDUCTIVE  LOGIC 

"  The  idols  of  the  den  are  those  of  each  individual ; 
for  everybody  (in  addition  to  the  errors  common  to 
the  race  of  man)  has  his  own  individual  den  or 
cavern  which  intercepts  and  corrupts  the  light  of 
nature,  either  from  his  own  peculiar  and  singular 
disposition,  or  from  his  education  and  intercourse 
with  others,  or  from  his  reading,  and  the  authority 
acquired  by  those  whom  he  reverences  and  admires, 
or  from  the  different  impressions  produced  on  the 
mind  as  it  happens  to  be  jDreoccupied  and  predis- 
posed, or  equable  and  tranquil,  and  the  like;  so 
that  the  spirit  of  man  (according  to  its  several  dis- 
positions) is  variable,  confused,  and  as  it  were  actu- 
ated by  chance ;  and  Heraclitus  said  well  that  men 
search  for  knowledge  in  lesser  worlds,  and  not  in 
the  greater  or  common  world. 

''There  are  also  idols  formed  by  the  reciprocal 
intercourse  and  society  of  man  with  man,  which  we 
call  idols  of  the  market,  from  the  commerce  and 
association  of  men  with  each  other;  for  men  con- 
verse by  means  of  language,  but  words  are  formed 
at  the  will  of  the  generality,  and  there  arises  from 
a  bad  and  unapt  formation  of  words  a  wonderful 
obstruction  to  the  mind.  Nor  can  the  definitions 
and  explanations  with  which  learned  men  are  wont 
to  guard  and  protect  themselves  in  some  instances, 
afford  a  complete  remedy,  —  words  still  manifestly 
force  the  understanding,  throw  everything  into  con- 
fusion, and  lead  mankind  into  vain  and  innumer- 
able controversies  and  fallacies. 

''^Lastly,  there  are  idols  which  have  crept  into 
men's  minds  from  the  various  dogmas  of  peculiar 


FALLACIES  271 

systems  of  philosophy,  and  also  from  the  perverted 
rules  of  demonstration,  and  these  we  denominate 
idols  of  the  theatre ;  for  we  regard  all  the  systems 
of  philosophy  hitherto  received  or  imagined,  as  so 
many  plays  brought  out  and  performed,  creating 
fictions  and  theatrical  worlds.  Nor  do  we  allude 
merely  to  general  systems,  but  also  to  many  ele- 
ments and  axioms  of  sciences  which  have  become 
inveterate  by  tradition,  implicit  credence,  and  neg- 
lect." ^ 

All  such  tendencies,  as  thus  presented  by  Bacon, 
clog  and  hamper  the  normal  functioning  of  the 
judgment.  The  mind  must  be  alert  and  on  guard 
to  eliminate  such  fatal  seeds  of  error. 

III.  Errors  due  to  the  Imagination. —  Here  the 
imagination  supplies  inner  connections  and  rela- 
tions, lying  beyond  the  sphere  of  observation,  in 
order  to  explain  the  nature  of  the  observed  x^he- 
nomena  themselves.  The  danger  here  is  that  the 
elements  supplied  in  order  to  make  the  self-con- 
sistent whole  do  not  correspond  to  reality.  The 
system,  regarded  as  a  mental  construction,  may  be 
complete  in  all  of  its  co-ordinated  parts,  and  never- 
theless possess  no  objective  reality.  Under  this 
head  fall  all  loosely  constructed  hypotheses.  In  the 
framing  of  an  hypothesis  in  general,  the  imagina- 
tion functions  very  largely.  It  is  the  inner  vision 
that  represents  to  the  mind  the  things  not  seen. 
Moreover,  the  imagination  is  peculiarly  liable  to 
error,  and  to  swing  clear  of  the  trammels  of  fact, 
and  in  the  region  of  pure  fancy  construct  systems 
1  Bacon,  Novum  Ch^gano7i,  Book  I.  Aphorisms  XXXIX.  etc. 


272  INDUCTIVE  LOGIC 

that  rest  upon  no  solid  basis  of  reality.  These 
dangers  in  detail  have  been  pointed  out  in  the 
chapter  on  "  Hypothesis." 

The  most  fertile  source  of  error,  however,  arises 
from  that  natural  elation  of  mind  upon  the  discov- 
ery even  of  slight  confirming  evidence  of  the  truth 
of  the  assumed  hypothesis.  This  enthusiasm  is  apt 
to  magnify  unduly  an  inadequate  verification,  and 
to  rest  satisfied  in  an  hypothesis  that  is  grounded 
upon  an  insufiicient  basis.  Thus  since  the  year 
1770  more  than  forty  discoveries  of  new  elementary 
substances  have  been  announced  to  the  world  by 
enthusiastic  experimenters,  and,  in  all  cases,  their 
discoveries  have  been  proved  to  be  absolutely  worth- 
less. For  instance,  it  was  confidently  announced 
that  Torbern  Bergmann,  in  1777,  had  extracted  from 
diamonds  what  he  considered  to  be  a  new  earth, 
and  called  it  "  terra  nobilis."  Wedgwood,  in  1790, 
discovered  "  australia  '^  in  sand  obtained  from  the 
continent  of  that  name  ;  but  Hatchett  proved  it 
to  be  merely  a  mixture  of  silica,  alumina,  oxide  of 
iron,  and  plumbago.  In  1805  Eichter  discovered 
"  niccolanium  "  ;  it  was  afterwards  proved  to  be  a 
mixture  of  iron,  cobalt,  nickel,  and  arsenic.  These 
instances  are  but  a  few  of  the  many  which  charac- 
terize the  history  of  chemical  research,  and  stand 
as  conspicuous  witnesses  of  the  danger  of  divorcing 
fancy  from  fact. 

The  imagination,  however,  properly  constrained  is 
most  potent  in  suggesting  possible  causal  relations, 
in  constructing  hypotheses,  in  devising  methods  of 
experiment  in  order  to  verify  them,  and  in  forming 


FALLACIES  27o 

universal  concepts  in  which  all  the  particulars  of 
observation  must  coinhere.  Davy  and  Faraday 
were  both  conspicuous  in  this  mental  characteristic. 
And  to  this  source  their  eminent  discoveries  may  be 
traced.  Dr.  Whewell  says,  for  instance,  of  Farar 
day  :  "  In  discovering  the  nature  of  voltaic  action, 
the  essential  intellectual  requisite  was  to  have  a  dis- 
tinct conception  of  that  which  Faraday  expressed 
by  the  remarkable  phrase,  '  A7i  axis  of  pov^er  hav- 
ing equal  and  oj)posite  forces.^  And  the  distinctness 
of  this  idea  in  Faraday's  mind  shines  forth  in  every 
part  of  his  writings.  He  appears  to  possess  the 
idea  of  this  kind  of  force  with  the  same  eminent 
distinctness  with  which  Archimedes  in  the  ancient 
and  Stevinus  in  the  modern  history  of  science  pos- 
sessed the  idea  of  pressure,  and  were  thus  able  to 
found  the  idea  of  mechanics.  And  when  Faraday 
cannot  obtain  these  distinct  modes  of  conception,  he 
is  dissatisfied  and  conscious  of  defect."  ^ 

It  is  indeed  a  touch  of  genius  that  enables  one  to 
grasp  and  formulate  a  central  idea  that  will  unify 
and  also  universalize  a  large  body  of  seemingly  dis- 
connected and  incongruous  facts.  But  such  an  idea 
must  be  the  expression  of  the  relations  actually  ob- 
taining, and  no  subjective  fancy  projected  upon  the 
phenomena  themselves,  however  clever  or  ingen- 
ious such  an  imaginative  creation  may  be.  If  one 
were  asked  what  is  the  most  efficient  instrument 
of  scientific  research,  the  answer  must  be,  "The 
Imagination  !  "     And  if  one  were  asked  what  is  the 

1  Whewell,  History  of  Inductive  Sciences,  Vol.  III.  3d  ed., 
p.  147. 

T 


274  INDUCTIVE   LOGIC 

most  fertile  source  of  error,  the  answer  likewise 
must  be,  "  The  Imagination  !  "  It  must  also  be 
remembered  that  it  is  not  sufficient  merely  that  an 
hypothesis  should  be  in  harmony  with  the  facts  in 
the  case  ;  it  must  be  proved  also  that  the  facts  are 
connected  with  the  hypothesis  through  necessary 
links. 

And  it  is  well  also  to  bear  this  in  mind  when 
arguing  against  a  rival  hypothesis  that  may  have 
been  advanced  by  an  opponent  who  has  claimed  for 
it  only  the  possibility  of  its  validity,  and  who  has 
not  affirmed  its  necessity.  It  is  manifestly  unfair, 
as  well  as  fallacious,  to  deny  the  possibility  of  the 
hypothesis  merely  by  indicating  certain  uncertain- 
ties connected  with  establishing  it.  To  contradict 
possibility,  one  must  prove  the  hypothesis  im- 
possible. Regarding  such  a  conflict  between  rival 
hypotheses  Ueberweg  suggestively  comments  as 
follows :  "  In  cases  of  this  kind,  it  is  one  of  the 
hardest  of  scientific  and  ethical  problems  to  give 
fair  play  to  one's  opponent.  Our  own  prejudices 
are  sure  to  influence  us.  Yet  the  effect  of  the  influ- 
ence of  another's  standpoint,  when  it  is  reached,  is 
of  immense  value  in  scientific  knowledge.  Polemic 
easily  leads  to  exasperation;  it  is  easy  both  to 
abuse  it,  and  to  let  it  alone  because  of  dislike  to 
the  conflicts  which  it  produces;  but  it  is  difficult 
to  recognize  it,  and  use  it  in  the  right  sense  as  the 
necessary  form  which  the  labor  of  investigation 
always  takes.  Man  never  attains  to  a  scientific 
knowledge  of  the  truth  without  a  rightly  conducted 
battle  of  scientifically  justifiable  hypotheses,  the  one 


FALLACIES  275 

against  the  other :  the  scientific  gnidance  of  this 
battle  is  the  true  dialectic  method.^'  ^ 

IV.  Errors  of  the  Conceptucd  Processes.  —  This 
class  of  errors  arises  in  the  formation  of  general 
concepts  and  their  expression  in  universal  laws. 
The  natural  tendency  of  the  mind  to  generalize 
often  leads  to  ill-considered  results.  The  universal 
unites  many  differences  into  an  identity,  and  the 
mind  will  readily  minimize  the  differences  in  order 
to  form  a  desired  universal;  thus  disparate  attri- 
butes may  be  incorrectly  co-ordinated  in  one  and 
the  same  system.  Herschel  has  remarked  that 
hasty  generalization  is  the  bane  of  science.  And 
Bacon  has  said  our  intellects  want  not  wings,  but 
rather  weights  of  lead  to  moderate  their  course. 

The  method  of  agreement,  when  relied  upon  to 
the  exclusion  of  further  experimental  determina- 
tion, is  a  fertile  source  of  error  in  this  respect.  The 
possibility  of  a  plurality  of  causes  should  be  ever 
kept  prominently  in  mind.  One  readily  assigns  an 
effect  to  a  causal  element  which  is  only  partially 
its  cause;  the  consequent  generalization  is,  there- 
fore, incorrect.  For  instance,  it  often  happens  that 
activities  of  young  animals  are  described  as  instinc- 
tive and  congenital ;  and  universal  propositions  are 
founded  thereupon.  And  yet  it  may  be  that  the 
activities  referred  solely  to  instinct  are  due  par- 
tially to  imitation.  In  order  to  avoid  this  error 
and  eliminate  the  factor  of  imitation,  investigators 
in  this  line  are  accustomed  to  study  the  activities 
of  animals  hatched  in  incubators  and  purposely 
1  Ueberweg,  A  System  of  Logic,  etc.,  p.  509. 


276  INDUCTIVE  LOGIC 

kept  from  all  of  tlieir  kind.  This  illustration  will 
serve  to  show  the  precautions  that  must  be  taken 
in  order  to  eliminate  all  possible  error  from  the 
data  which  the  process  of  generalization  constructs 
into  universal  forms.  So  also  inaccuracies  in  any 
of  the  other  inductive  methods  lead  to  gross  errors 
in  the  consequent  generalizations  based  upon  them. 
Under  this  head,  also,  are  the  fallacies  resulting 
from  the  extension  of  empirical  laws  to  spheres 
beyond  the  experience  which  they  embody  and 
express.  This  source  of  error  is  especially  illus- 
trated in  laws  expressing  some  quantitative  relation 
between  antecedent  and  consequent ;  it  is  a  natural 
supposition  in  such  cases,  and  yet  a  very  mislead- 
ing one  oftentimes,  that  a  simple  proportional  rela- 
tion will  exist  between  phenomena  of  the  same, 
but  with  greater  or  lesser  magnitude  as  the  case 
may  be.  Bacon  gives  the  following  illustrations  of 
this  fallacy :  "  Suppose  a  leaden  ball  of  a  pound 
weight,  let  fall  from  a  steeple,  reaches  the  earth  in 
ten  seconds,  will  a  ball  of  two  pounds,  where  the 
power  of  natural  motion,  as  they  call  it,  should  be 
double,  reach  it  in  five?  No,  they  will  fall  almost 
in  equal  times,  and  not  be  accelerated  according  to 
quantity.  Suppose  a  drachm  of  sulphur  would 
liquefy  half  a  pound  of  steel,  will,  therefore,  an 
ounce  of  sulphur  liquefy  four  pounds  of  steel  ?  It 
does  not  follow ;  for  the  stubbornness  of  the  matter 
in  the  patient  is  more  increased  by  quantity  than 
the  activity  of  the  agent.  Besides,  too  much  as 
well  as  too  little  may  frustrate  the  effect, — thus, 
in  smelting  and  refining  of  metals  it  is  a  commou 


FALLACIES  277 

error  to  increase  the  heat  of  the  furnace  or  the 
quantity  of  the  flux;  but  if  these  exceed  a  due 
proportion,  they  prejudice  the  operation  because 
by  their  force  and  corrosiveness  tliey  turn  much  of 
the  pure  metal  into  fumes,  and  carry  it  off,  whence 
there  ensues  not  only  a  loss  in  the  metal,  but  the 
remaining  mass  becomes  more  sluggish  and  intract- 
able. Men  should,  therefore,  remember  how  ^sop's 
housewife  w^as  deceived,  who  expected  that  by 
doubling  her  feed  her  hen  should  lay  two  eggs  a 
day;  but  the  hen  grew  fat  and  laid  none.  It  is 
absolutely  unsafe  to  rely  upon  any  natural  experi- 
ment before  proof  be  made  of  it,  both  in  a  less  and 
a  larger  quantity."  ^ 

Another  fallacy  of  the  same  order  often  occurs  in 
the  inference  concerning  the  interpolated  elements 
of  a  series  whose  successive  values  have  not  all  been 
observed.  The  inference  extends  the  nature  of  the 
known  to  the  unknown  parts,  and  presumes  that 
the  intermediate  links  betw^een  actually  observed 
parts  of  the  series  are  in  accordance  with  the 
general  nature  of  the  latter.  Such  inferences  very 
often  give  correct  results,  as,  in  the  plotting  of  a 
curve,  some  salient  points  may  be  determined  ac- 
cording to  observed  quantitative  variations,  and  the 
remaining  portions  supplied,  as  upon  the  above 
supposition.  This  extension  to  cover  intermediate 
and  unobserved  instances  may,  however,  be  some- 
times very  fallacious.  For  a  force  may  be  assumed 
to  be  such  that  its  effects  increase  steadily,  and  it 

1  Bacon,  Advancement  of  Learning^  Book  V.  Chapter  II. 
p.  190. 


278  INDUCTIVE  LOGIC 

may  be  that  they  operate  periodically ;  interpola- 
tion upon  one  assumed  basis  when  the  other  is  the 
true  one,  would  of  course  introduce  grave  errors. 
To  eliminate  such  errors,  devices  have  in  many 
cases  been  resorted  to  by  which  a  self-registering 
apparatus  will  record  all  successive  values  of  the 
phenomena  under  investigation. 

Under  the  fallacies  of  hasty  generalization,  nat- 
urally fall  all  provincialisms  which  arise  from  a 
narrow  nature  and  habit  of  mind.  The  local  tradi- 
tions and  superstitions,  the  prevailing  winds,  the 
social  customs  and  manners,  are  taken  as  types  of  a 
universal  experience.  The  inferential  widening  of 
the  circle  of  a  limited  experience  is  always  provo- 
cative of  false  inference  and  misleading  results. 

We  have  also  false  analogies  which  consist  in  the 
extension  of  our  experience  of  certain  phenomena 
that  we  have  observed  to  be  alike  in  some  respects 
to  include  other  attributes  not  observed,  concern- 
ing which  we  assume  a  corresponding  similarity; 
the  abuse  of  final  causes  may  be  regarded  as  a 
special  case  of  false  analogy.  Moreover,  a  tendency 
to  consider  causation  in  the  light  exclusively  of  final 
causes  has  often  retarded  the  advance  of  science,  in 
withdrawing  the  attention  and  energies  of  the  in- 
vestigator from  a  search  after  physical  causes,  as,  for 
instance,  among  the  ancients  it  was  declared  that 
the  leaves  of  the  trees  are  to  defend  the  fruit  from 
the  sun  and  wind.  Resting  satisfied  in  such  an 
explanation,  the  precise  function  of  the  leaves  in 
the  economy  of  the  plant's  growth  was  not  further 
investigated,  and  thus  progress  was  impossible. 


FALLACIES  279 

Again,  incorrect  classification  is  a  source  of  error. 
In  grouping  together  disi^arate  phenomena,  we  have 
a  basis  for  forming  a  generic  concept  that  will  in- 
clude incompatible  species,  or,  in  other  words,  a 
universal  that  will  have  evident  exceptions.  More- 
over, if  the  classification  is  partial,  the  resulting 
laws  based  upon  it  will  have  only  empirical  force. 

I  have  endeavored  in  this  chapter  to  indicate 
errors  that  are  mainly  psychological  in  their  origin, 
for  two  reasons.  In  the  first  place,  such  errors 
operate  as  disturbing  forces  in  the  midst  of  purely 
logical  processes.  The  data  of  inference  are  psy- 
chological as  regards  their  source,  and  errors  thus 
originating  affect  the  inference  based  upon  them, 
appearing  in  the  final  result  as  logical  fallacies. 
An  error  of  observation  becomes  an  error  in  the 
judgment  that  is  based  upon  the  original  percep- 
tion, and  perdures  in  the  hypothesis,  classification, 
etc.,  founded  on  that  judgment,  and  finally  emerges 
in  the  conclusions  based  upon  these  processes.  In 
the  second  place,  the  fallacies  that  are  purely 
formal,  and  in  the  strict  sense  logical,  are  not  as 
apt  to  deceive  and  mislead  the  mind.  In  the 
material  data  especially  lurk  the  germs  of  fallacy. 
On  the  theory  that  it  is  wiser  and  also  more  logical 
to  stamp  out  an  error  in  its  incipiency,  I  have 
placed  special  emphasis  upon  the  various  psycho- 
logical processes  as  initial  sources  of  error.  More- 
over, it  is  more  rational  to  deal  with  errors  of  pro- 
cess rather  than  flaws  of  product.  A  machine  that 
turns  out  imperfect  articles  could  have  its  imperfec- 
tions rectified  by  repairing  each  article  thus  pro- 


280  INDUCTIVE  LOGIC 

duced;  or  the  iiiaehine  itself  could  be  readjusted 
so  as  to  produce  the  articles  without  flaw.  It  is 
needless  to  say  which  method  is  the  more  logical, 
and  most  satisfactory,  as  well. 

The  desideratum  is  accurate  and  comprehensive 
observation ;  a  discriminating  judgment  formed  in 
the  "  dry  light "  of  reason ;  an  imagination  that  has 
deep  insight  into  the  heart  of  surface  appearances ; 
and  powers  of  generalization  which  transcend  ob- 
served phenomena  by  adequately  interpreting  them. 


CHAPTEE   XVIII 

The    Inductive   Methods   as    Applied    to   the 
Various  Sciences 

The  nature  of  each  separate  science  will  deter- 
mine certain  peculiarities  of  metliod  for  that  sci- 
ence ;  and  its  peculiar  method  will  be  largely  a 
matter  of  growth,  as  experience  accredits  or  dis- 
credits the  various  results  which  its  operation  may 
attain.  It  will  thus  be  corrected  or  supplemented 
according  as  it  stands  the  test  of  achieved  results. 
There  are,  however,  some  general  features,  and  es- 
pecially some  natural  limitations  of  the  inductive 
methods,  that  may  be  properly  indicated. 

I.  In  the  first  place,  the  nature  of  the  method 
used,  and  its  efficiency,  as  measured  by  its  results, 
will  be  found  to  vary  as  the  nature  of  the  phe- 
nomena themselves.  Some  phenomena  admit  of 
analysis  and  further  determination  by  experiment. 
Instead  of  attempting  to  determine  the  relation  of 
a  complex  antecedent  to  a  complex  consequent,  the 
antecedent  is  first  separated  into  its  component 
parts,  and  one  element  is  tested  alone  in  order  to 
determine  its  precise  effect.  The  relation  can  then 
be  expressed  between  the  simple  antecedent  and 
simple  consequent,  as  a  causal  connection;  and  it 
281 


282  INDUCTIVE  LOGIC 

admits,  moreover,  of  a  quantitative  determination  as 
well.  Such  a  method  of  procedure  by  analytical  ex- 
periment enables  us  to  rise  to  laws  having  universal 
validity.  This  method  is  characteristic,  especially, 
of  the  physical  sciences,  because  the  phenomena 
readily  admit  of  resolution  into  component  parts, 
and  the  isolation  of  one  simple  force  so  as  to  de- 
termine its  total  effect.  The  physical  forces  are 
most  readily  adaptable  to  experiment.  They  there- 
fore afford  the  widest  field  for  the  application 
of  the  experimental  method  of  inductive  inquiry. 
Moreover,  we  may  readily  f)redict  the  results  of  a 
combination  of  simple  forces,  when  we  know  the 
laws  governing  their  component  elements.  The 
inducto-deductive  method,  therefore,  becomes  es- 
pecially efficient  in  extending  the  domain  of  the 
physical  sciences.  Here,  also,  mathematical  analy- 
sis and  calculation  is  most  valuable  as  an  aid  to 
experimental  investigation,  and  in  determining 
quantitative  relations  as  necessitated  by  the  math- 
ematical laws  to  which  the  data  gathered  induc- 
tively must  conform. 

There  are,  however,  sciences  which  present  phe- 
nomena of  such  a  high  degree  of  complexity  that 
an  analysis  of  a  complex  Avhole  into  its  separate 
parts  or  elements  of  force  is  impossible.  More- 
over, the  phenomena  cannot  be  analyzed  in  this 
respect  either,  that  a  certain  part  of  the  complex 
whole  can  be  indicated  as  the  whole  antecedent, 
and  the  remaining  portion  as  the  entire  conse- 
quent. The  difficulty,  therefore,  is  twofold;  it 
is  impossible  to  separate  the  complex  whole  into 


INDUCTIVE  METHODS   AND  THE   SCIENCES      283 

two  other  complex  wholes,  antecedent  and  conse- 
quent, and  still  further  impossible  to  separate  such 
antecedent  and  consequent,  even  if  they  could  be 
determined,  into  their  simplest  component  parts. 
The  phenomena  presented  are  here  not  in  the 
form  of  a  sequence  so  often  as  in  that  of  coexist- 
ence, as  in  the  sciences  of  botany,  zoology,  and  the 
like.  Here  the  methods  of  analogy  and  classifica- 
tion must  be  resorted  to,  and  we  obtain  descriptive 
laws  as  the  result. 

The  forces  manifested  in  the  processes  of  vital 
growth  are  especially  difficult  to  determine  by  ex- 
periment; for  they  not  only  operate  to  produce 
certain  effects,  but  perdure  in  the  effects  to  pro- 
duce certain  other  effects  in  a  process  of  con- 
tinuous construction.  Separation  by  mechanical 
analysis  means  instant  cessation  of  the  process 
itself.  Dissection  means  death.  Here,  then,  is  a 
natural  limitation.  Moreover,  the  laws  of  devel- 
opment are  further  modified  by  external  changes. 
The  result  of  the  inner  force  and  the  outer  in- 
fluences, working  together,  complicates  the  prob- 
lems to  such  an  extent  that  the  pure  inductive 
methods  are  well-nigh  impossible  of  application. 
Kesort  is  then  had  to  determination  by  statistical 
methods.  Large  groups  of  plants  and  animals  are 
examined  for  the  purpose  of  noting  tendencies 
disclosed  in  the  aggregate,  but  hidden  as  regards 
their  manifestation  in  the  individual.  Here,  of 
course,  classification  is  an  aid  in  disclosing  simi- 
larities and  differences  that  may  suggest  hypoth- 
eses to  explain  certain  dominant  characteristics. 


284  INDUCTIVE  LOGIC 

We  may,  moreover,  have  merely  permanent  ef- 
fects presented  in  perception,  the  cause  having 
ceased  to  act  long  since.  Thus  in  geology  we  have 
facts  that  have  been  caused,  it  is  true,  but  the 
causes  can  be  discerned  only  as  manifested  in 
the  effects,  and,  therefore,  they  can  be  determined 
only  by  the  method  of  hypothesis,  which  may 
lead  to  verification  or  not,  as  the  case  may  be. 
Again,  certain  sciences  may  suggest  problems 
which  concern  the  explanation  or  significance, 
not  of  particular  phenomena  within  the  sphere 
of  that  science,  but  rather  the  interpretation  of  the 
whole  body  of  phenomena  which  the  science  in 
question  comprehends.  The  problem  is  not  solved, 
therefore,  by  any  attempt  in  the  way  of  analysis 
by  experiment,  but  rather  in  the  way  of  synthesis 
through  hypothesis ;  that  is,  the  ideal  construction 
of  a  whole  which  will  unify  and  account  for  all 
facts,  or,  in  other  words,  to  discern  the  system 
which  underlies  and  co-ordinates  the  various  par- 
ticular manifestations.  This  is  seen  especially 
illustrated  in  the  problems  which  geology  and  bi- 
ology present  concerning  the  interpretation  of  their 
respective  phenomena  regarded  in  the  light  of 
their  totality.  Astronomy  also  presents  a  mass 
of  seemingly  chaotic  phenomena,  and  yet  the  aim 
of  this  science  is  to  reduce  them  all  to  some  one 
self-consistent  system. 

For  instance,  Mr.  Spencer  remarks  concerning  the 
geologist :  "  He  does  not  take  for  his  problem  only 
those  irregularities  of  the  earth's  crust  that  are 
worked  by  denudation ;  or  only  those  which  igneous 


INDUCTIVE  METHODS   AND  THE  SCIENCES      285 

action  causes.  He  does  not  seek  simply  to  under- 
stand how  sedimentary  strata  were  formed ;  or  how 
faults  were  produced ;  or  how  moraines  originated ; 
or  how  the  beds  of  Alpine  lakes  were  scooped  out. 
But  taking  into  account  all  agencies  co-operating 
in  endless  and  ever-varying  combinations,  he  aims 
to  interpret  the  entire  structure  of  the  earth's  crust. 
If  he  studies  separately  the  action  of  rain,  rivers, 
glaciers,  icebergs,  tides,  waves,  volcanoes,  earth- 
quakes, etc.,  he  does  so  that  he  may  be  better 
able  to  comprehend  their  joint  actions  as  factors 
in  geological  phenomena ;  the  object  of  his  science 
being  to  generalize  these  phenomena  in  all  their 
involved  connections  as  parts  of  one  whole."  Mr. 
Spencer  also  describes  the  nature  of  biology  in 
much  the  same  way.  ^^  In  like  manner  biology 
is  the  elaboration  of  a  complete  theory  of  life 
in  each  and  all  of  its  involved  manifestations.  If 
different  aspects  of  its  phenomena  are  investi- 
gated apart,  if  one  observer  busies  himself  in 
classing  organisms,  another  in  dissecting  them, 
another  in  ascertaining  their  chemical  composi- 
tions, another  in  studying  functions,  another  in 
tracing  laws  of  modification,  —  they  are  all  con- 
sciously or  unconsciously  helping  to  work  out 
a  solution  of  vital  phenomena  in  their  entirety, 
both  as  displayed  by  individual  organisms  and 
by  organisms  at  large."  ^ 

Mr.   Spencer  makes  the  distinction  between  in- 
vestigation of  particular  causal    relations   on   the 
one  hand,  and,  on  the  other,  the  interpretation  of 
1  Spencer,  Classification  of  the  Sciences,  pp.  19,  20. 


286  INDUCTIVE  LOGIC 

the  total  phenomena  of  a  science  as  the  basis 
of  classification  of  the  sciences.  He  divides  the 
sciences  into  those  which  treat  of  the  forms  in 
which  phenomena  are  known,  such  as  the  Abstract 
Sciences  of  mathematics  and  logic  (i.e.  formal 
logic) ;  and  those  which  treat  of  the  phenomena 
themselves  or  the  Concrete  Sciences.  The  latter 
redivide  into  the  Abstract  Concrete  Sciences,  so 
called,  because  the  specific  elements  of  the  con- 
crete phenomena  are  abstracted  from  the  phe- 
nomena, considered  as  a  whole,  and  so  determined 
as  causal  laws,  relative  to  particular  references 
within  the  whole  body  of  phenomena  which  the 
science  comprehends;  these  are  such  sciences  as 
mechanics,  physics,  chemistry,  etc. :  the  second  is 
that  of  the  Concrete  Sciences  simply,  which  re- 
gard phenomena  in  their  totalities,  as  above  de- 
scribed. A  difference  of  method  is  here  indicated. 
The  Abstract  Concrete  Series  are  to  be  investigated 
analytically,  that  is,  by  experiment  principally, 
with  a  view  of  exhibiting  complex  phenomena 
in  their  simplest  terms.  The  simple  Concrete 
Sciences  are  to  be  treated  synthetically,  that  is, 
by  the  framing  of  an  hypothesis  that  will  com- 
prehend all  particular  phenomena  in  one  co-ordi- 
nated whole. 

The  division  of  Herbert  Spencer  can  only  be 
accepted  in  a  general  way  as  indicating  pre- 
dominant characteristics  of  the  two  kinds  of  sci- 
ences. It  will  not  do  to  lay  down  hard  and  fast 
lines  here,  for  every  science  presents  two  kinds 
of    problems;  the   first,   to    determine    particular 


INDUCTIVE  METHODS  AND  THE  SCIENCES      287 

causal  relations ;  the  second,  to  co-ordinate  all  such 
relations  into  a  self-consistent  system  which  will 
unify  all  separate  and  individual  instances.  For 
instance,  take  the  phenomena  of  light  in  physics. 
Particular  problems  as  regards  intensity,  velocity, 
composition  of  light,  etc.,  present  themselves ; 
then  an  underlying  problem.  How  explain  all 
the  phenomena  of  light  upon  some  one  single 
basis  regarding  the  essential  nature  of  light. 
Hence  arose  the  emission  and  undulatory  theories 
of  light,  and  all  phenomena  bearing  upon  the 
theory  were  marshalled  in  support  of  one  and 
of  the  other,  until  the  conflict  was  conclusively 
decided.  And  again,  the  theory  of  light,  the 
theory  of  electricity,  the  theory  of  heat,  etc., 
suggest  still  another  problem.  How  unify  all  the 
separate  theories  in  one  all-comprehensive  theory 
to  which  the  separate  phenomena  may  be  alike 
referred.  Thus  every  science  presents  particular 
problems,  and  a  general  problem  as  well.  And 
herein  lies  a  suggestion  that  all  investigators  in 
any  branch  of  science  would  do  Avell  to  bear  in 
mind.  Specialization  in  any  one  line  of  particular 
problems  should  always  lead  to  a  consideration 
of  the  relations  of  these  particular  problems  to  the 
general  system  of  which  they  are  parts.  Special- 
ization that  does  not  thus  supply  its  own  corrective 
by  the  natural  insistence  of  the  mind  to  interpret 
the  particular  in  the  light  of  more  general  laws, 
tends  to  narrowness  of  mind  and  barren  results. 

II.    In  reference   to   method   in   the  sciences  it 
must  be  observed  also  that  in  certain  phenomena 


288  INDUCTIVE  LOGIC 

the  simple  theory,  which  regards  the  causal  con- 
nection as  a  transfer  of  energy  according  to  the 
doctrine  of  the  conservation  of  energy,  is  further 
complicated  by  certain  variations  and  modifications 
of  the  energy  in  the  process  of  transference.  When, 
for  instance,  a  billiard-ball  strikes  another,  and  the 
second  ball,  by  virtue  of  the  impact,  receives  the 
energy  of  the  initial  moving  ball  transferred  to  it, 
the  problem  is  simplified  by  the  fact  that  the  motion 
of  the  first  is  easily  traceable  in  the  second,  being 
a  transfer  of  energy  which  manifests  itself  in  the 
same  manner  in  the  two  cases.  However,  the  prob- 
lem is  complicated  at  once  when  in  chemistry,  for 
instance,  the  two  combining  elements  form  a  third 
in  which  the  characteristic  features  of  the  former 
are  wholly  lost  in  the  new  form.  Here  is  likewise 
a  transfer  of  energy,  which  may  have  mechanical 
equivalents,  it  is  true,  and  yet  so  radical  a  change  of 
form  accompanies  the  transfer  that  it  complicates 
the  problems  which  arise  in  this  science.  AVe  have 
seen  how  the  combined  inducto-deductive  method 
often  predicts  events  and  the  nature  of  phenomena 
not  yet  observed.  And  yet  this  becomes  most  dif- 
ficult whenever  transfer  of  energy  is  accompanied 
by  a  change  in  the  peculiarities  of  its  manifestation 
as  well.  Knowledge  of  the  nature  of  two  elements, 
and  all  their  separate  characteristics,  will  not  be 
sufficient  data  for  any  prediction  as  to  the  nature 
of  the  compound.  Thus  chemistry  confronts  a 
natural  difficulty  as  regards  method,  which  does  not 
affect  physical  science  generally. 

Another  difficulty  appears  in  psychology,  for  here 


INDUCTIVE   METHODS  AND  THE  SCIENCES      289 

stimuli  from  the  outer  world,  expressed  in  terms  of 
physical  energy  and  quantitatively  determined,  pro- 
duce psychical  reactions,  that  cannot  be  expressed 
in  physical  terms.  And,  on  the  other  hand,  proc- 
esses of  ideation  produce  muscular  activities,  that 
may  be  estimated  in  physical  terms.  It  has  been 
urged  that  here  the  theory  of  conservation  of  energy 
breaks  down,  that  the  transferred  energy  is  wholly 
accounted  for  by  the  nerve  and  brain  modifications, 
and  that  the  psychical  accompaniments  are  wholly 
unaccounted  for  upon  this  basis.  They  stand  out 
as  unexplored  remainders. 

This  objection  is  met  in  two  ways.  One  is 
that  the  physical  and  psychical  are,  as  it  were, 
two  closed  circles,  and  while  simultaneous  in  their 
functioning  do  not  mutually  interact.  This  is 
the  theory  of  the  so-called  "  psychophysical  paral- 
lelism." It  necessitates  metaphysical  explanations 
and  postulates  that  seem  to  complicate  rather  than 
simplify  the  difficulties.  The  second  is  the  more 
reasonable,  that  psychical  activity  may  be  radically 
different  from  physical  and  yet  the  two  capable  of 
reacting  upon  each  other,  so  as  to  liberate  the 
potential  activities  in  either  sphere,  and  thus  ini- 
tiate a  series  of  causally  connected  phenomena. 
Such  a  theory  is  buttressed  by  substantial  analogies 
in  the  physical  sphere  itself;  namely,  that  in  many 
phenomena  the  impinging  force  is  so  modified,  by 
the  reaction  due  to  the  nature  of  the  substance  acted 
upon,  as  to  lose,  to  all  observation  at  least,  its  orig- 
inal characteristic  features.  For  instance,  friction 
passes  over  into  electricity  because  of  the  nature  of 


290  INDUCTIVE  LOGIC 

the  substance  that  is  rubbed ;  thunder  sours  cream, 
and  thus  sound  vibrations  cause  effects  wholly 
incongruous  to  them. 

These  illustrations  might  be  multiplied  through 
all  the  realm  of  physical  science.  They  are  so 
many  as  to  prepare  us  for  realizing  the  possibility, 
at  least,  that  physical  excitations  may  produce 
psychical  phenomena  in  the  sense  that  the  outer 
stimulus  calls  into  activity  psychical  energies,  that 
thus  stirred,  manifest  themselves  according  to  the 
forms  of  their  own  nature,  rather  than  the  forms 
of  the  physical  phenomena  exciting  them.  Upon 
such  a  theory  we  may  proceed,  by  observation  and 
experiment,  to  measure  duration,  intensity,  etc.,  of 
mental  reactions  responding  to  external  stimuli. 
As  regards  the  method  here  employed,  the  series  is 
considered  as  one  and  complete,  so  that  physical 
excitations  are  traced,  as  it  were,  through  an  un- 
broken causal  chain  to  their  psychical  effects,  and 
vice  versa.  On  the  theory  of  two  closed  circles,  it 
is  difficult  to  indicate  a  logical  method  of  experi- 
mental inquiry,  unless  it  be  further  postulated  that 
activities  in  the  one,  according  to  its  kind,  may 
induce  modifications  of  the  other  according  to  its 
kind.     This  reservation  is  generally  insisted  upon. 

III.  It  sometimes  happens  that  the  phenomena 
of  one  science  are  to  be  interpreted  in  the  light  of 
the  results  of  another  science.  Thus  the  laws  of 
one  science  become  guiding  principles  in  investi- 
gating the  causal  relations  existing  in  another 
sphere.  This  can  only  be  done  when  there  is  some 
similarity  between  the  phenomena  of  the  two  sci- 


INDUCTIVE  METHODS  AND  THE  SCIENCES      291 

ences.  This  method  is  especially  illustrated  in  his- 
torical explanation.  The  problem  presents  a  mass 
of  events  that  must  be  co-ordinated  in  a  system 
wherein  their  several  ca,usal  relations  will  be  ex- 
hibited. And  not  merely  must  detached  epochs  be 
proved  causally  interrelated  as  regards  the  events 
occurring  in  them,  but  here,  also,  the  special  prob- 
lems give  rise  to  a  general  problem,  to  discover  in 
the  whole  the  philosophy  of  history,  and  to  deter- 
mine the  several  historical  tendencies  in  one  system 
whose  characteristic  features  will  reveal  the  fact  that 
"through  the  ages  one  increasing  purpose  runs." 

To  solve  the  special  and  the  general  problems  of 
history,  recourse  is  had  to  an  analysis  of  events  on 
the  basis  of  well-established  psychological  results. 
The  phenomena  of  history  are  substantially  the 
activities  of  man,  both  in  his  individual  and  col- 
lective capacities.  Events  being  given,  an  hypothe- 
sis concerning  the  motives,  and  ends  which  actuated 
them,  is  framed  upon  the  supposition  that  men  ordi- 
narily are  impelled  by  similar  motives  under  similar 
circumstances,  in  order  to  achieve  similar  ends. 
Here  the  analogies  drawn  between  men  of  the 
present  and  men  of  the  past,  or  between  men  mov- 
ing in  the  ordinary  routine  of  e  very-day  life  and 
men  whose  acts  may  be  epoch-making,  furnish  a 
basis  for  historical  interpretation.  We  say  that 
a  series  of  events,  perhaps  of  a  very  complicated 
nature,  can  be  explained  only  by  an  hypothesis  that 
a  well-defined  purpose  and  a  strong  determined  will 
were  fashioning  them  and  moving  through  them  to 
an  end  that  was  in  the  chief  actor's  mind  from  the 


292  INDUCTIVE  LOGIC 

beginning.  And  so  the  rise  of  social  habits,  cus- 
toms, traditions,  laws,  the  religion,  the  government, 
and  national  institutions  of  a  people  have  an  origin  in 
psychical  and  not  physical  elements,  a  deeper  under- 
standing of  whose  nature  and  all  that  it  necessitates 
tends  to  a  clearer  elucidation  of  the  problems  therein 
presented.  The  knowledge  of  man,  the  microcosm, 
is  a  guiding  thread  amid  the  bewildering  mazes  of 
the  macrocosm.  It  is  possible,  of  course,  for  the 
imagination  of  the  historian  to  lead  him  to  wander 
far  afield,  and  invent  fanciful  motives,  purposes, 
public  policies,  etc.,  to  explain  given  events.  How- 
ever, here,  as  in  the  physical  and  other  sciences,  the 
hypotheses  framed  must  meet  the  general  require- 
ments and  conditions  of  a  valid  hypothesis. 

IV.  There  has  been  a  growing  tendency  in  sciences 
regarded  as  solely  or  largely  deductive,  to  correct 
and  supplement  the  traditional  method  and  results 
by  a  more  searching  inductive  inquiry.  This  is 
especially  true  of  political  economy.  The  deductive 
method  proceeded  to  build  up  a  body  of  doctrine 
composed  of  inferences  necessitated  by  a  few  fun- 
damental premises.  The  premises  were  such  as 
the  following:  The  principal  motive  of  action 
is  self-interest;  the  earth,  as  man's  great  supply- 
house,  is  limited  in  extent  and  productivity;  the 
physical  and  psychological  tendencies  of  man  lead 
him  to  multiply  his  own  species  with  a  rapid- 
ity which,  if  not  counteracted  by  obstacles,  would 
bring  about  an  unlimited  increase  of  population. 
All  economic  laws  were  thus  deduced  from  some 
such  fundamental  propositions  as  these.      The  re- 


INDUCTIVE  METHODS  AND  THE  SCIENCES     293 

suits  of  this  deductive  method,  however,  have 
been  brought  to  the  bar  of  another  method  for 
searching  examination  and  judicial  sentence.  In 
1848  Hildebrand,  and  Knies  in  1853,  with  Eoscher 
in  1854,  set  forth  the  principles  of  the  historical 
school  of  political  economy.  They  held  that  an 
inductive  inquiry  must  be  started  in  order  to 
estimate  the  physical,  ethnical,  and  historical  con- 
ditions of  a  nation  and  its  stage  of  civilization. 
These  forces,  correctly  assessed,  will  give  the  eco- 
nomic conditions  of  a  particular  period  of  history, 
or  of  a  particular  nation.  This  is  not  the  place  to 
criticise  the  tenets  of  this  school,  but  merely  to 
point  out  the  fact  that  its  influence  has  been  potent 
in  correcting  and  supplementing  the  results  ob- 
tained in  a  purely  deductive  manner. 

Deduction  may  give  the  joint  effect  of  universal 
psychological  impulses,  operative  under  certain  nat- 
ural conditions  of  environment,  etc.,  provided  no 
disturbing  force  is  present.  But  the  question  here 
is  not  whether  a  certain  cause,  if  acting  alone,  will 
produce  a  certain  effect ;  but  whether  counteracting 
causes  will  be  present,  or  modifying  causes,  as  the 
case  may  be.  To  estimate  the  results  of  collocations 
and  not  simple  causes  becomes,  as  we  have  seen,  a 
complex  problem.  For  its  solution  recourse  must 
be  had  largely  to  statistical  methods  whereby  large 
aggregates  reveal  tendencies  that  are  actual  and  not 
theoretical  merely. 

In  a  similar  way,  the  historical  school  of  juris- 
prudence, associated  with  Savigny,  has  influenced 
the  so-called  philosophical  school  in  demonstrating 


294  INDUCTIVE   LOGIC 

that  results  theoretically  determined  by  deduction 
are  constantly  modified  by  the  real  conditions  and 
limitations  of  each  particular  nation's  life.  The 
influence  of  this  school  is  indicated  by  a  significant 
fact,  that  when  Hegel  wrote  his  theory  of  law 
(Eechtslehre)  he  paid  more  regard  to  the  historical 
formation  of  states  than  did  the  earlier  theorists 
of  natural  law.^ 

Again,  another  illustration  of  the  growing  prev- 
alency  of  inductive  method  is  found  in  the  mod- 
ern psychological  method.  The  sole  method  was 
considered  from  time  immemorial  to  be  that  of 
introspection.  Its  results,  however,  were  meagre; 
the  method  itself  was  indefinite  and  lacked  cer- 
tainty and  uniformity.  Inductive  inquiry,  there- 
fore, proceeded  by  its  own  methods  to  secure  and 
interpret  material  in  other  and  various  fields.  As 
Professor  Ladd  says:  '^The  method  of  psycholog- 
ical science  is  peculiarly  introspective  and  analytic 
of  the  envisaged  phenomena  called  states  of  con- 
sciousness. But  it  is  far  broader  and  more  effective 
than  it  could  be  if  it  were  merely  introspective. 
It  pushes  its  analysis  of  the  genesis  of  the  j^he- 
nomena  as  far  back  as  x^ossible,  by  the  use  of 
experimental  methods,  and  methods  of  external 
observation  applied  to  the  whole  process  of  mental 
evolution  (study  of  infants,  of  primitive  man,  and 
of  the  lower  animals,  —  evolutionary  and  compara- 
tive psychology).  It  interprets  the  psychological 
life  of  the  individual  mind  in  the  light  of  knowl- 
edge gathered  concerning  the  psychical  development 

1  Bluntschli,  The  Theonj  of  the  State,  p.  69. 


INDUCTIVE  METHODS   AND  THE   SCIENCES      295 

of  the  race  (the  psychological  study  of  literature, 
society,  art,  religion,  etc.).  It  lays  peculiar  empha- 
sis upon  abnormal  and  pathological  phenomena  of 
the  nervous  and  mental  life  (psychiatry,  hypnotism, 
phenomena  of  insanity  and  of  the  criminal  classes, 
etc.).  It  takes  account  of  the  rise  and  fall  of  par- 
ticular forms  of  psychological  theory  (the  history 
of  psj^chology).  It  strives  to  transcend  experience 
by  hypothetical  principles  of  explanation.  But  in 
the  employment  of  all  these  methods  this  science 
differs  in  no  important  respect  from  the  sciences 
which  deal  wholly  with  physical  phenomena.  It 
is  only  the  use  of  introspection  for  the  possession, 
and,  to  some  extent  at  least,  for  the  analysis,  of 
its  objects,  which  makes  psychology,  as  respects 
its  method,  different  from  the  other  sciences."  ^ 

In  the  above,  we  see  that  inductive  inquiry  lays  all 
possible  fields  of  research  under  tribute  to  the  one 
end  of  explaining  and  correlating  psychical  phenom- 
ena. The  systems  of  ethics  also,  which  are  founded 
upon  an  a  priori  basis,  are  becoming  more  indebted 
to  empirical  investigations  which  have  given  a  richer 
content  to  the  strictly  formal  ethic.  Advanced 
psychological  research,  the  study  of  race  character- 
istics, tribal  customs,  habits,  law,  religion,  etc.,  the 
indications  of  moral  progress,  —  all  give  material 
which,  if  interpreted  by  right  hypotheses,  will 
throw  light  upon  the  theory  of  ethical  principles 
regarded  merely  from  a  speculative  point  of  view. 
We  may  conclude,  therefore,  that  the  inductive 
method  and  the  deductive  are  not  mutually  exclu- 
1  Ladd,  Introduction  to  Philosophy ,  p.  116. 


296  INDUCTIVE  LOGIC 

sive  processes.  They  may  be  so  combined  as  mu- 
tually to  strengthen  one  another.  AVhat  Bluntschli 
says  of  jurisprudence  may  be  applied  equally  as 
well  to  all  sciences  that  claim  some  a  priori  basis : 
"The  old  strife  between  the  philosophical  and 
historical  schools  in  Germany  has  altogether  ceased. 
Peace  was  made  as  early  as  1840.  Since  then  it  is 
recognized  on  all  sides  that  the  experiences  and 
phenomena  of  history  must  be  illumined  with  the 
light  of  ideas,  and  that  speculation  is  childish  if  it 
does  not  consider  the  real  conditions  of  the  nation's 
life."  1 

It  will  be  seen  how  important  a  factor  historical 
data  becomes,  in  all  the  sciences  that  deal  with 
human  volition  and  activities.  Whatever  hypoth- 
esis may  be  framed,  it  must  correspond  to  these  data, 
because  they  represent  actual  conditions  that  must 
be  co-ordinated  in  a  self-consistent  system,  and  their 
nature  and  relations  satisfactorily  interpreted. 

1  Bluntschli,  The  Theo?^  of  the  State,  p.  70. 


CHAPTEE  XIX 
Historical  Sketch  of  Induction 

Socrates  (470-399  b.c).  — We  find  the  beginnings 
of  inductive  inquiry  in  the  Socratic  or  maieatic 
method,  that  art  of  mental  midwifery  by  which 
conceptions  were  to  be  delivered  from  the  mass  of 
individual  experiences  and  opinions  in  which  they 
lie  concealed.  The  Socratic  procedure  in  the  forma- 
tion of  conceptions  is  to  question  every  particular 
view,  and  estimate  it  by  bringing  together  analogous 
cases,  and  discovering  their  natural  connections,  so 
as  to  explicate  the  general  notion  which  it  contains, 
and  thus  proceed  from  comparison  of  particulars  to 
the  framing  of  general  propositions.  Socrates'  gen- 
eralizations were  many  of  them  hasty,  and  in  his 
desire  to  formulate  a  general  conception  he  over- 
looked exceptions  and  minimized  difficulties,  but  in 
his  method  there  were  the  germs  of  truly  scientific 
procedure.  The  sphere  of  his  method  was,  however, 
limited,  as  he  applied  it  only  to  the  illumination  of 
ethical  controversies. 

Plato  (427-347  b.c). — Plato  enriched  the  Socratic 
method  of  induction  by  removing  its  limitation  to 
ethical  inquiry.  Plato  was  especially  concerned 
with  investigating  the  relations  of  his  "  ideas  "  to 
each  other,  and  this  led  to  the  apprehension  of  the 
297 


298  INDUCTIVE  LOGIC 

logical  relations  between  conceptions,  especially  as 
regards  their  subordination  and  co-ordination.  This 
forms  a  basis  for  classification,  —  Plato's  division  of 
class-concepts  or  logical  genera  into  their  species  is  a 
prominent  feature  of  his  method.  He  also  suggests 
the  hypothetical  method  of  treating  the  relations  of 
concepts ;  namely,  to  examine  a  tentatively  proposed 
conception  by  developing  all  the  possible  conse- 
quences that  would  follow  from  its  union  with  known 
conceptions.  This  is  in  keeping  with  the  inducto- 
deductive  method  of  Mill  and  the  modern  logicians. 
Aristotle  (384-322  b.c).  —  Aristotle's  name  is  es- 
pecially, and  it  may  be  said  almost  exclusively, 
associated  with  deductive  logic  and  syllogistic 
reasoning.  Although  he  did  not  develop  fully 
the  inductive  logic,  he  nevertheless  did  not  ignore 
it,  in  some  of  its  essential  features  at  least.  He 
acknowledged  the  necessity  of  investigating  the 
starting-point  of  deduction,  namely,  the  ultimate 
grounds  of  proof,  and  of  the  principles  of  explana- 
tion. This  process  he  called  dialectic.  It  is  a 
double  process  that  proceeds  from  the  particulars 
given  in  perception,  and  from  the  ideas  current  in 
customary  opinion,  to  discover  the  general,  and 
then  from  the  general  to  deduce  the  particular, 
which  is  thereby  verified  in  the  process.  The 
former  procedure  is  the  reverse  of  the  deductive, 
and  is  epagogic  or  inductive.  Induction,  according 
to  him,  is  a  syllogism  in  which  the  inference  that 
the  major  belongs  to  the  middle,  is  mediated 
through  the  minor  directly ;  and  not  indirectly 
through  the  middle.     Thus,  to  use  Aristotle's  illus- 


HISTORICAL  SKETCH  OF  INDUCTION  299 

tration,  tlie  investigation  of  the  connection  between 
the  absence  of  gall  in  animals  and  longevity  in  a 
number  of  instances,  as  in  man,  horse,  mule,  etc., 
may   disclose   their   coexistence.^     They  are   then 
imited  directly  without  mediation  of  a  middle  term. 
If  we  had  given  the  universal  proi^osition  to  start 
with,  AVhatever  animal  has   no  gall  is  long-lived, 
and  the  minor  premise  that  man,  horse,  mule,  etc., 
are  animals  having   no   gall,  then   the   conclusion 
would  follow,  therefore  they  are  long-lived.     This 
is  the  deductive  syllogism.     The  inductive  method, 
on  the  other  hand,  starts  from  particular  observa- 
tion that  the  horse  which  has  no  gall  is  long-lived, 
so    also   the   mule,   so   also   man,   etc. ;   therefore, 
without  any  middle  term,  a  coexistence  is  taken 
as  equivalent  to  a  causal  relation  between  these 
attributes,  and  the  inference  is  drawn  that  all  ani- 
mals having  no  gall  are  long-lived.     Such  an  infer- 
ence is  valid  syllogistically,  however,  only  on  the 
assumption  that  the  instances  examined  comprise 
the  whole  class  having  the  attributes  under  investi- 
gation.     This   inductive    syllogism,  therefore,  ex- 
presses inferences  only  of  complete  enumeration. 
The  form  of  such  a  syllogism  is  as  follows :  — 

Let  ^S'  =  minor  term, 

P=  major  term, 
M=  middle  term. 
This,  that,  and  the  other  >S  is  P. 
This,  that,  and  the  other  S  is  all  M. 
.-.   Alll/isP. 

1  Aristotle,  Prior  Analytics,  II.  xxiii. 


300  INDUCTIVE  LOGIC 

Here  it  will  be  observed  that  the  particular  in- 
stances comprising  the  minor  term  /S,  when  summed 
up,  equal  the  middle  term.  There  is  no  inference 
in  this  if  we  have  regard  to  the  strict  sense  in 
which  the  word  is  used.  Aristotle,  indeed,  consid- 
ered the  only  scientific  induction  to  be  the  so-called 
perfect  induction,  and  says  that  to  generalize  many 
experiences  of  the  same  kind  is  admissible  only 
when  there  is  no  contrary  case.  The  thought  that 
causal  connection  enables  us  to  generalize  is  stated 
by  Aristotle,  but,  as  Ueberweg  says,  it  "does  not 
attain  to  a  fundamental  significance  in  his  logical 
theory."  ^ 

The  Precursors  of  Bacon. — The  revolt  against 
the  scholasticism  of  the  Middle  Ages  and  the 
fetters  of  the  Aristotelian  logic  was  many-voiced, 
culminating,  however,  as  regards  the  emphasis 
placed  upon  induction  as  a  scientific  method,  in  the 
works  of  Francis  Bacon. 

Foremost  among  the  early  champions  of  induc- 
tive inquiry  we  find  Koger  Bacon,  born  in  1214, 
a  Franciscan  monk,  yet  devoted  heart  and  mind 
to  the  cause  of  science.  His  Ojnis  Majus  was 
published  first  in  1733  by  Dr.  S.  Jebb,  principally 
from  a  manuscript  in  the  library  of  Trinity  College, 
Dublin.  This  work  is  characterized  by  a  spirit  of 
protest  against  authority  in  general,  and  that  of 
Aristotle  and  his  logic  especially.  He  recom- 
mends mathematics  and  experiment  as  the  two 
great  instruments  of  scientific  investigation.  In 
this  particular  it  is  interesting  to  note  his  antici- 
1  Ueberweg,  Logic,  p.  479. 


HISTORICAL  SKETCH  OF  INDUCTION  301 

pation  of  the  modern  matliematico-physica]  modes 
of  scientific  inquiry.  Tlie  following  quotation  will 
give  an  indication  of  his  spirit  and  aims :  — 

"  Experimental  science,  the  sole  mistress  of  spec- 
ulative sciences,  has  three  great  prerogatives  among 
other  parts  of  knowledge:  First,  she  tests  by  ex- 
periment the  noblest  conclusions  of  all  other  sci- 
ences ;  next,  she  discovers,  respecting  the  notions 
which  other  sciences  deal  with,  magnificent  truths 
to  which  these  sciences  of  themselves  can  by  no 
means  attain ;  her  third  dignity  is,  that  she  by  her 
own  power,  and  without  respect  of  other  sciences, 
investigates  the  secrets  of  nature."  ^ 

Leonardo  da  Vinci  (1452-1519).  —  Leonardo  com- 
bined in  one  personality  many  brilliant  talents,  be- 
ing eminent  as  sculptor,  painter,  architect,  engineer, 
astronomer,  and  natural  philosopher.  His  works, 
unpublished,  exist  in  manuscripts  in  the  library  of 
the  Institute  at  Paris.  He  expresses  himself  very 
clearly  and  emphatically  concerning  the  relation  of 
experience  to  speculation :  "  Theory  is  the  general ; 
experiments  are  the  soldiers.  We  must  consult  ex- 
perience, and  vary  the  circumstances  till  we  have 
drawn  from  them  general  rules ;  for  it  is  she  who 
furnishes  true  rules.  But  of  what  use,  you  ask,  are 
these  rules  ?  I  reply,  that  they  direct  us  in  the 
researches  of  nature  and  the  operations  of  art. 
They  prevent  our  imposing  upon  ourselves  and 
others,  by  promising  ourselves  results  which  we 
cannot   obtain.      But   see   the   absurdity   of   men ! 

1  Whewell,  Philosophy  of  the  Inductive  Sciences,  Vol.  II. 
p.  333. 


302  INDUCTIVE  LOGIC 

They  turn  up  their  noses  at  a  man  who  prefers  to 
learn  from  nature  herself  rather  than  from  authors 
who  are  only  her  clerks."  ^  This  latter  remark  is 
similar  in  its  reference  to  the  epithet  of  Galileo, 
applied  to  men  whose  knowledge  comes  wholly 
from  books  and  not  from  observation;  namely, 
"paper  philosophers." 

Bernardinus  Telesius  (1508-1588).  —  His  work,  en- 
titled De  Rerum  Natura,  anticipated,  in  some  degree 
at  least,  the  Novum  Organon  of  Bacon.  Bacon 
himself  says  of  him :  "  We  think  well  concerning 
Telesius,  and  acknowledge  him  as  a  lover  of  truth, 
a  useful  contributor  to  science,  an  amender  of 
some  tenets,  the  first  of  recent  men."  Telesius 
set  for  himself  a  high  aim  and  purpose,  but  in 
the  application  of  his  method  he  was  not  so  fortu- 
nate, being  dominated  in  his  researches  by  specu- 
lation rather  than  the  results  of  experimental 
inquiry.  As  to  his  professed  method,  he  announces 
in  the  title  of  his  De  Natura  that  "  the  construction 
of  the  world,  the  magnitude  and  nature  of  the 
bodies  contained  in  it,  are  not  to  be  investigated  by 
reasoning,  which  was  done  by  the  ancients,  but  are 
to  be  apprehended  by  the  senses  and  collected  from 
the  things  themselves."  And  in  the  Proem  of  the 
same  work  he  says  in  the  same  strain  that  "  they 
who  before  us  have  inquired  concerning  the  con- 
struction of  this  world,  and  of  the  things  which  it 
contains,  seem  indeed  to  have  prosecuted  their  ex- 
amination with  protracted  vigils  and  great  labor, 

1  Whewell,  Philosophy  of  the  Inductive  Sciences,  Vol.  II. 
p.  369. 


HISTORICAL  SKETCH  OF   INDUCTION  303 

but  never  to  have  looked  at  it.  For,  as  it  were, 
attempting  to  rival  God  in  wisdom,  and  venturing 
to  seek  for  the  principles  and  causes  of  the  world 
by  the  light  of  their  own  reason,  and  thinking  they 
had  found  what  they  had  only  invented,  they  made 
an  arbitrary  world  of  their  own.  AVe  then,  not 
relying  on  ourselves,  and  of  a  duller  intellect  than 
they,  propose  to  ourselves  to  turn  our  regards  to 
the  world  itself  and  its  parts." 

Following  Telesius,  and  of  his  school,  was  Thomas 
Campanella  (1568-1639).  He  was  a  contemporary 
of  Bacon,  and,  under  the  influence  of  Telesius,  early 
conceived  the  idea  of  an  inductive  method  of  re- 
search. At  the  age  of  twenty-two,  he  published  a 
work  whose  character  may  be  judged  by  its  title, — 
"  Thomas  Campanella's  Philosophy  demonstrated 
to  the  senses,  against  those  who  have  philosophized 
in  an  arbitrary  and  dogmatical  manner,  not  taking 
nature  for  their  guide ;  in  which  the  errors  of  Aris- 
totle and  his  followers  are  refuted  from  their  own 
assertions  and  the  laws  of  nature ;  and  all  the 
imaginations  feigned  in  the  place  of  nature  by  the 
Peripatetics  are  altogether  rejected ;  with  a  true 
defence  of  Bernardin  Telesius  of  Cosenza,  the 
greatest  of  philosophers  ;  confirmed  by  the  opin- 
ions of  the  ancients,  here  elucidated  and  defended, 
especially  those  of  the  Platonists." 

The  ideas  of  Bacon,  with  their  impetus  to  the 
inductive  method  of  research,  were  not  only  antici- 
pated by  writers  of  books  ;  but  actual  discoveries 
by  zealous  investigators  were  turning  the  attention 
of  the  thinking  world  to  nature  and  her  secrets. 


304  INDUCTIVE  LOGIC 

There  was  an  illustrious  line  of  pioneers  in  this 
undiscovered  country.  There  was  Andrew  Ceesal- 
pinus  (1520-1603),  the  founder  of  the  science  of 
botany ;  and  earlier,  Copernicus  (1473-1543),  ad- 
vancing his  heliocentric  theory;  and  Gilbert  (1540- 
1603),  the  court  physician  of  Elizabeth  and  James, 
conducting  with  untiring  perseverance  his  investi- 
gations of  the  nature  of  magnetism  and  electricity. 
Kepler,  born  ten  years  after  Bacon,  1571,  and 
Galileo,  born  in  1564,  and  their  contemporary, 
Tycho  Brahe,  born  in  1546,  formed  a  triumvirate 
of  scientific  power  and  brilliancy,  made  resplendent 
by  the  glory  of  the  heavens  itself.  It  must  be 
remembered,  too,  that  at  this  time  a  new  world  had 
been  discovered  across  the  seas ;  the  recent  inven- 
tions of  gunpowder,  of  the  mariner's  compass,  and 
of  the  art  of  printing,  all  tended  to  stimulate  the 
thought  of  the  world,  and  usher  in  a  new  epoch  in 
the  history  of  civilization. 

Francis  Bacon  (1561-1626).  —  Bacon's  inductive 
system  is  given,  for  the  most  part,  in  the  Novum 
Organon.  The  title  of  this  work  was  in  itself  a 
protest  against  Aristotle  and  his  logic,  implying 
that  Aristotle's  Organon  was  now  out  of  date  and 
was  to  be  superseded  by  the  new.  Bacon  insists  that 
all  knowledge  of  nature  has  for  its  end  the  disclos- 
ing of  the  causes  of  things.  According  to  the  Aris- 
totelian scheme,  causes  are  formal,  material,  efficient, 
or  final.  Bacon  is  only  concerned  with  the  formal 
causes.  For,  he  says,  all  events  have  their  ground 
in  the  "  forms "  of  things.  By  the  form  of  a 
thing,  he   meant  its  essential  nature.     Where  he 


HISTORICAL  SKETCH  OF  INDUCTION  305 

uses  the  form  we  may  well  supply  the  word 
law.  To  discover  the  forms  of  phenomena,  it  is 
necessary,  according  to  Bacon,  to  collect  as  many  in- 
stances as  possible  in  which  the  phenomenon  under 
investigation  appears ;  together  they  form  a  tabula 
prmsentm.  In  like  manner,  the  instances  in  which 
the  phenomenon  is  lacking  are  grouped  in  a  tabula 
absentice;  and  a  third  group  must  be  formed,  —  a 
tabula,  graduum  in  which  the  variations  of  intensity 
in  the  phenomena  are  compared  with  the  varying 
intensity  of  other  phenomena.  The  i^roblem  is 
then  to  be  solved  by  a  process  of  exclusion  (exclu- 
sio) ;  that  is,  the  rejection  or  exclusion  of  the  several 
qualities  which  are  not  found  in  some  instance 
where  the  given  'quality  is  present,  or  are  found  in 
some  instance  where  the  given  quality  is  absent, 
or  are  found  to  increase  in  some  instance  where  the 
given  quality  decreases,  or  to  decrease  when  the 
given  quality  increases.  By  this  process  an  indica- 
tion will  be  given  by  which  an  hypothesis  may  be 
framed,  and  finally  verified  by  subsequent  observa- 
tion and  experiment.  In  the  sketch  of  this  method 
it  will  be  seen  that  his  three  tables  of  instances 
closely  resemble  the  methods  of  agreement,  of 
difference,  and  of  concomitant  variations.  They, 
however,  lack  the  precision  of  the  later  formula- 
tion of  these  methods.  There  is  no  hint  at  a  syste- 
matic selection  and  variation  of  the  instances ;  and 
no  requirement,  as  in  the  method  of  difference, 
that  two  instances  shall  be  so  experimentally  de- 
termined that  they  will  agree  in  every  point  save 
the  given  phenomenon,  which  is  present  in  the  one 

3C 


306  INDUCTIVE   LOGIC 

and  absent  from  the  other.  Bacon,  however,  made 
a  substantial  contribution  to  the  method  of  induc- 
tion in  general,  in  insisting  upon  the  examination 
of  instances  themselves,  and  in  ascending  from 
them  quite  gradually  the  scale  of  the  more  general 
up  to  the  most  general,  and  in  this  he  entered  a 
vigorous  protest  against  hasty  generalization. 

As  to  the  manner  of  certifying  the  hypothesis 
formed  after  the  process  of  collecting  and  sifting 
instances,  Bacon  has  no  recourse  to  deduction 
based  upon  the  hypothesis  and  consequent  verifica- 
tion. He  seems  to  despise  mathematical  method 
as  an  ally  of  inductive  inquiry ;  and,  therefore,  has 
no  place  in  his  scheme  for  the  prediction  of  new 
phenomena  by  means  of  calculation.  Of  his  nine 
divisions  of  aids  to  induction,  he  completed  only 
the  first,  —  Prerogative  Instances.  Of  the  instances 
which  he  enumerates,  twenty-seven  in  all,  only  a 
few  have  any  bearing  directly  upon  the  inductive 
method  proper.  Two  sets  of  these  instances  may 
be  considered  as  a  crude  statement  of  the  methods 
of  agreement  and  difference ;  the  Solitary  Instances, 
which  either  exhibit  a  phenomenon  Avithout  any  of 
its  usual  accompaniments  or  which  agree  in  every- 
thing except  some  particular  phenomenon,  and 
Migratory  Instances,  where  qualities  are  produced 
in  bodies  by  evident  causes,  as,  for  instance,  the 
producing  of  whiteness  by  pounding  glass,  also  by 
stirring  water  into  froth.  These  instances,  how- 
ever, as  exhibited  by  Bacon,  lack  precision  and  the 
possibilities  of  accurate  determination  of  causal  con- 
nections.    The  only 'Other  group  of  instances  hav- 


HISTORICAL  SKETCH  OF  INDUCTION  307 

ing  special  inductive  significance  is  that  of  the  In- 
stantia  Crucis;  as  before  mentioned,  such  instances 
are  valuable  in  deciding  between  rival  hypotheses. 
With  all  the  deficiencies  of  Bacon's  method,  how- 
ever, his  service  to  the  thinking  world  is  indispu- 
table, in  emphasizing  the  need  of  investigating 
phenomena  themselves  as  a  corrective  of  fanciful 
speculations,  and  in  his  vigorous  warnings  against 
prejudice,  against  intellectual  indolence,  against 
subjection  of  the  mind  to  the  trammels  of  author- 
ity,  and  against  over-hasty  generalizations. 

Locke  (1632-1704).— Locke  applied  the  method 
of  Bacon  to  the  objects  of  inner  experience.  He 
declared  that  the  data  of  all  knowledge  come  from 
sensation,  or  sense-perception,  and  from  reflection, 
and  that  there  are  no  "innate  ideas,"  and  there- 
fore no  starting-point  for  a  priori  speculations 
The  method  that  had  been  found  useful  m  actual 
discoveries,  such  as  those  of  Newton,  Kepler,  and 
others,  Locke  insisted  would  prove  productive  also 
of  rich  results  in  the  intellectual  sphere. 

Isaac  Newton  (1642-1727).  -  Scientific  method 
was  gradually  formulating  itself  in  the  actual  pur- 
suits of  scientific  investigation,  -  not  thought  out 
as  much  as  worked  out,  and  its  efficiency  tested  and 
confirmed  by  results.  Newton  gives  form  to  that 
which  was  a  result  of  many  experiments,  and  ot  a 
mass  of  various  experiences,  in  his  Rules  of  Phi- 
losophizing {Begulm  Philosophandi)  prefixed  to  the 

Principia. 

These  rules  are  as  follows :  — 
1.  The  first  rule  is  twofold :  — 


308  INDUCTIVE  LOGIC 

a.  "Only  real  causes  are  to  be  admitted  in  ex- 
planation of  phenomena." 

h.  "  No  more  causes  are  to  be  admitted  than  such 
as  suffice  to  explain  the  phenomena." 

2.  "  In  as  far  as  possible,  the  same  causes  are  to 
be  assigned  for  the  same  kind  of  natural  effects." 

3.  ''Qualities  that  can  neither  be  increased  nor 
diminished  in  intensity,  and  that  obtain  in  all 
bodies  accessible  to  experiment,  must  be  considered 
qualities  of  all  bodies  Avhatsoever." 

4.  ''In  philosophical  experiment,  propositions 
collected  from  phenomena  by  induction  are  to 
be  held,  notwithstanding  contrary  hypotheses,  as 
either  exactly  or  approximately  true,  until  other 
phenomena  occur  whereby  they  are  either  rendered 
more  exact  or  are  proved  liable  to  exceptions." 

Newton's  celebrated  saying,  "Hypotheses  non 
fingo,"  was  originally  a  protest  against  the  sup- 
position of  the  existence  of  occult  or  imaginary 
causes  to  explain  phenomena,  notably  the  Car- 
tesian explanation  of  the  celestial  movements  by 
vortices.  Hypotheses  of  a  different  nature,  and 
rationally  grounded  of  course,  did  not  fall  under 
Newton's  reprehension. 

Sir  John  Herschel  (1792-1871).  —Herschel's  Dis- 
course on  the  Study  of  Natural  Philosophy  was  pub- 
lished in  1832.  John  Stuart  Mill  reviewed  this  book 
in  the  Examiner  and  was  evidently  impressed  and 
influenced  by  it.  Herschel's  design  was  to  make 
the  methods  of  science  more  explicit.  These  are 
contained  in  nine  "  propositions  readily  applicable 
to  particular  cases,  or  rules  of  philosophizing." 


HISTORICAL  SKETCH  OF   INDUCTION  309 

Of  these  propositions,  the  second,  seventh,  eighth, 
and  ninth  present  substantially  the  experimental 
methods  as  afterwards  more  precisely  formulated 
by  Mill.  These  methods,  however,  he  regards  sim- 
ply as  means  to  discovery,  and  not  methods  of 
proof.  Of  the  remaining  propositions,  the  first 
is  a  more  precise  statement  of  Bacon's  principle 
of  exclusion,  and  is  the  foundation  of  the  joint 
method  of  agreement  and  difference.  The  third 
proposition  is  that  "  we  are  not  to  deny  the  exist- 
ence of  a  cause  in  favor  of  which  we  have  a 
unanimous  agreement  of  strong  analogies,  though 
it  may  not  be  apparent  how  such  a  cause  can  pro- 
duce the  effect,  or  even  though  it  may  be  difficult 
to  conceive  its  existence  under  the  circumstances 
of  the  case."  The  fourth  is  that  "contrary  or 
opposing  facts  are  equally  instructive  for  the  dis- 
covery of  causes  with  favorable  ones."  The  fifth 
recommends  the  "  tabulation  of  facts  in  the  order 
of  intensity  in  which  some  peculiar  quality  sub- 
sists." The  sixth  rule  insists  upon  the  investi- 
gator keeping  prominently  in  mind  the  possibility 
that  '•' counteracting  or  modifying  causes  may  sub- 
sist unperceived,"  and  that  this  fact  may  be  the 
means  of  explaining  many  apparent  exceptions. 

Herschel  also  emphasizes  the  necessity  of  com- 
bining induction  and  deduction  in  complicated  in- 
quiries; and,  further,  he  explains  the  nature  of 
empirical  laws,  as  also  the  nature  and  tests  of 
hypotheses.  We  can  now  see  that  the  body  of  in- 
ductive principles  begins  at  length  to  assume  final 
form  and  proportion. 


310  INDUCTIVE   LOGIC 

Whewell  (1795-1866).  — Dr.  Wliewell  published 
his  Philosophy  of  the  Inductive  Sciences  in  1840, 
containing  his  system  of  induction.  His  method  in- 
volves two  principal  processes,  —  the  colligation  of 
facts  and  the  explication  of  conceptions.  The  inves- 
tigator is  to  gather  all  the  facts  at  his  dis^^osal,  and 
upon  them  he  is  to  superinduce  a  conception  which 
will  unify  them,  or  colligate  them.  He  says  these 
conceptions  are  supplied  by  the  mind,  while  facts  are 
supplied  by  the  sense.  This,  however,  is  a  distinc- 
tion that  sej)arates  so  widely  the  spheres  of  the 
particular  facts,  and  the  general  conceptions,  that 
upon  such  a  basis  a  union  of  the  two  as  explaining 
one  by  the  other  would  be  artificial  and  with  no 
corresponding  bond  of  reality.  The  colligating 
conception  does  not  exist  in  the  mind  before  or 
apart  from  its  existence  in  fact.  The  attempt  to 
fit  facts  to  ready-made  conceptions  is  of  the  nature 
of  guess-work.  Kepler's  nineteen  guesses  regarding 
planetary  orbits  is  an  instance  of  attempting  to 
superinduce  conceptions  upon  a  mass  of  facts.  It 
is  not  a  truly  scientific  or  logical  procedure,  and 
the  great  danger  of  applying  it  lies  in  the  fact 
that  the  mind  all  too  readily  tends  to  mould  facts 
into  the  forms  of  prior  conceptions. 

"The  Methods  employed  in  the  Formation  of 
Science,"  the  title  of  his  concluding  chapter,  are 
three,  as  follows:  Methods  of  Observation,  Meth- 
ods of  Obtaining  Clear  Ideas,  and  Methods  of 
Induction.  The  last  principally  concerns  our 
present  purposes.  The  methods  of  induction  are 
methods  of  discovery  rather  than  proof,  save  the 


HISTORICAL  SKETCH  OF  INDUCTION  311 

last,  wliicli   is  one  of  the  experimental  methods. 
They  are  the  method  of  curves  to  express  graphi- 
cally the  graduated  results  of  several  observations ; 
the   method  of   means,  and  the   method   of   least 
squares,  both  designed  to  eliminate  accidental  ac- 
companiments  of  constant   causes   by  striking  an 
average  of  several  observations ;  and  the  method  of 
residues.     Whewell's  method  may  be  characterized 
in  brief  as  a  method  of  discovery  rather  than  proof. 
John   Stuart    Mill   (1806-1873).  — Mill's    Logic, 
published   in   1843,  was   essentially  a  method   of 
proof  rather  than  a  method  of  discovery.     His  aim 
in  formulating  the  methods  in  vogue  in  experimen- 
tal science,  was  to  discover  the  precise  modes  of 
their  operation  in  order  to  apply  the  same  in  inves- 
tigating the  various  mental,  moral,  social,  and  polit- 
ical phenomena.     Bacon  in  the  Novum  Organon  had 
asserted  that  this  inductive  method  was  applicable 
to  the  intellectual  and  moral  sciences.     This  was  no 
doubt  suggestive  to  Mill,  as  it  had  been  to  Locke. 
Whately's  Logic,  published  in  1827,  influenced  Mill, 
and  was  the  means  of  turning  his  attention  to  logi- 
cal studies.    Whately's  book  was  reviewed  by  Mill, 
when  only  twenty-one,  in  the  Westmi7ister  Review. 
The   revival   in  logical   interest  at  this   time   and 
the  departure  from  scholastic  traditions  have  been 
traced  to  the  influence  of  Edward  Copleston,  tutor 
at   Oxford,   and   afterwards   Bishop    of    Llandaff. 
Whately's  work   represented   the   first-fruits,   and 
Mill's  the  richer  and  riper  product  of  this  revival 
of   logic.     It   is  a   matter   of   more   than   passing 
interest  to  note  that  one  of  Whately's  most  active 


312  INDUCTIVE  LOGIC 

collaborators  in  the  work  was  John  Henry  Newman, 
so  that,  as  Professor  Minto  says,  ^'  the  common  room 
of  Oriel,  which  Mr.  Fronde  describes  as  the  centre 
from  which  emanated  the  High  Church  Movement, 
may  also  be  said  to  have  been  the  centre  from  which 
emanated  the  movement  that  culminated  in  the  rev- 
olution of  logic." 

Mill's  special  office  as  regards  induction  consists 
in  his  crystallizing  the  principles  and  practices  of  the 
scientific  investigators  who  had  caught  and  reflected 
the  spirit  of  modern  research.  The  formulated  meth- 
ods of  inductive  logic,  substantially  as  given  by  Mill, 
have  become  the  recognized  methods  of  all  investi- 
gation that  is  actuated  by  a  scholarly  spirit  and  a 
scientific  habit.  Mill's  contributions  to  the  induc- 
tive logic  have  been  so  largely  drawn  from  and  so 
frequently  referred  to  in  the  composition  of  this 
book,  as  to  need  no  further  comment  here.  The 
works  of  the  more  recent  writers,  as  Lotze,  Sigwart, 
Bosanquet,  Jevons,  Venn,  etc.,  have  also  been  noticed 
in  the  body  of  the  text.  Their  work  is  largely  crit- 
ical, and  no  distinct  inductive  system  is  especially 
associated  with  any  of  their  names. 


CHAPTER   XX 

Logical  Exercises 

In  tlie  following  examples,  indicate  the  nature 
of  the  inferences,  the  methods  employed,  and  the 
character  of  the  results  obtained,  whether  valid 
or  invalid,  and  the  reasons  for  the  same. 

1.  In  all  unhealthy  countries  the  greatest  risk  of 
fever  is  run  by  sleeping  on  shore.  Is  this  owing  to 
the  state  of  the  body  during  sleep,  or  to  a  greater 
abundance  of  miasma  at  such  times?  It  appears 
certain  that  those  who  stay  on  board  a  vessel, 
though  anchored  at  only  a  short  distance  from 
the  coast,  generally  suffer  less  than  those  actually 
on  shore.  —  Darwin  in  Voyage  of  Naturalist. 

2.  That  the  period  of  the  tide  should  be  acciden- 
tally the  same  as  that  of  the  culmination  of  the 
moon,  that  the  period  of  the  highest  tide  should  be 
accidentally  the  same  as  that  of  the  syzygies,  is 
possible  m  abstracto  ;  but  it  is  in  the  highest  degree 
improbable;  the  far  more  probable  assumption  is, 
either  that  sun  and  moon  produce  the  tide,  or  that 
their  motion  is  due  to  the  same  grounds  as  the 
motion  of  the  tide. 

3.  In  measuring  the  velocity  of  sound  by  experi- 
ments conducted  at  night  with  cannon,  the  results 

313 


314  INDUCTIVE  LOGIC 

at  one  station  were  never  found  to  agree  exactly 
with  those  at  the  other.  Moreover,  it  was  noticed 
that  on  the  nights  when  the  discordance  was  great- 
est, a  strong  wind  was  blowing  nearly  from  one 
station  to  the  other. 

4.  M.  Melloni,  observing  that  the  maximum 
point  of  heat  is  transferred  farther  and  farther 
towards  the  red  end  of  the  spectrum,  according 
as  the  substance  of  the  prism  is  more  and  more 
permeable  to  heat,  inferred  that  a  prism  of  rock- 
salt,  which  possesses  a  greater  power  of  transmit- 
ting the  calorific  rays  than  any  known  body,  ought 
to  throw  the  point  of  greatest  heat  to  a  consider- 
able distance  beyond  the  visible  part  of  the  spec- 
trum ;  and  his  prediction  w^as  verified  by  subsequent 
experiment. 

5.  During  the  middle  of  the  eighteenth  century 
Bonnet  and  Spallanzani  discovered  that  the  horns, 
tails,  legs,  eyes,  or  even  head  of  some  creatures,  if 
cut  off,  would  grow  again.  The  tail  and  legs  of  a 
salamander  were  removed  and  reproduced  them- 
selves eight  times  in  succession.  By  means  of  a 
number  of  experiments  it  has  been  found  that  the 
more  simple  the  structure  of  an  animal  is,  the 
more  do  its  several  parts  possess  a  power  of  inde- 
pendent existence,  and  that  in  the  more  complex 
animals,  the  derangement  of  one  part  much  more 
affects  the  action  of  the  entire  organism. 

6.  Professor  Jevons  has  observed  that  economic 
crises  have  occurred  at  regular  intervals  of  about  ten 
years.  This  ten-year  periodicity,  moreover,  seems  to 
correspond  to  a  similar  periodicity  of  bad  harvests ; 


LOGICAL  EXERCISES  315 

and  the  cause  of  this  seems  to  be  a  decennial  peri- 
odicity in  the  spots  on  the  sun. 

7.  What  is  the  significance  of  the  remark  of 
Chevreul,  the  French  scientist:  ^' Every  fact  is  an 
abstraction." 

8.  Also  of  the  following  remark  of  M.  Espinas : 
"  If  human  activity  was  incompatible  with  the  order 
of  things,  the  act  of  boiling  an  egg  would  have  to  be 
regarded  as  a  miracle." 

9.  It  had  long  been  known  that  grasshoppers 
and  crickets  have  on  their  anterior  legs  two  pecul- 
iar, glassy,  generally  more  or  less  oval,  drum-like 
structures ;  but  these  were  supposed  by  the  older 
entomologists  to  serve  as  resonators,  and  to  rein- 
force or  intensify  the  well-known  chirping  sounds 
which  they  produce.  Johannes  Mliller  was  the 
first  who  suggested  that  these  drums  or  tympana 
act  like  the  tympanum  of  our  own  ears,  and  that 
they  are  really  the  external  parts  of  a  true  audi- 
tory apparatus.  That  any  animal  should  have  its 
ears  in  its  legs  sounds,  no  doubt,  a  priori,  very 
unlikely,  and  hence  probably  the  true  function  of 
this  organ  was  so  long  unsuspected.  —  Sir  John 
Lubbock. 

10.  In  simple  fracture  of  the  ribs,  if  the  lung 
be  punctured  by  a  fragment,  the  blood  effused  into 
the  pleural  cavity,  though  freely  mixed  with  air, 
undergoes  no  decomposition.  Why  air  introduced 
into  the  pleural  cavity  through  a  wounded  lung 
should  have  such  wholly  different  effects  from  that 
entering  directly  through  a  wound  in  the  chest  was 
to  me  a  complete  mystery  until  I  heard  of  the  germ- 


316  INDUCTIVE  LOGIC 

theory  of  putrefaction,  when  it  at  once  occurred  to 
me  that  it  was  only  natural  that  air  should  be  fil- 
tered of  germs  by  the  air-passages,  one  of  whose 
offices  is  to  arrest  inhaled  particles  of  dust  and 
prevent  them  from  entering  the  air-cells.  —  Pro- 
fessor Lister. 

11.  If  the  lungs  be  emptied  as  perfectly  as  pos- 
sible and  a  handful  of  cotton-wool  be  placed  against 
the  mouth  and  nostrils,  and  you  inhale  through  it, 
it  will  be  found  on  expiring  this  air  through  a  glass 
tube  that  its  freedom  from  floating  matter  is  mani- 
fest. The  application  of  this  is  obvious ;  if  a  phy- 
sician wishes  to  hold  back  from  the  lungs  of  his 
patient,  or  from  his  own,  the  germs,  or  virus  by  which 
contagious  disease  is  propagated,  he  will  employ  a 
cotton- w^ool  respirator.  —  Professor  T yndall. 

12.  In  the  desert  of  North  Africa,  where  neither 
trees,  brushwood,  nor  even  undulation  of  the  surface 
afford  the .  slightest  protection  to  its  foes,  a  modifi- 
cation of  color  in  animals  which  shall  be  assimilated 
to  that  of  the  surrounding  country  is  absolutely 
necessary.  Hence,  without  exception,  the  upper 
plumage  of  every  bird,  whether  lark,  chat,  sylvian, 
or  sand-grouse,  and  also  the  fur  of  all  the  smaller 
mammals  and  the  skin  of  all  snakes  and  lizards,  is 
of  one  uniform  isabelline,  or  sand  color.  —  Wallace. 

13.  Darwin,  in  investigating  the  difference  in 
weight  between  cross  and  self  fertilized  plants, 
found  that  the  six  finest  crossed  plants  averaged 
108.16  ounces,  whilst  the  six  finest  self  fertilized 
plants  averaged  only  23.7  ounces  or  as  100  to  22. 

14.  Bees  incessantly  visit  the  flowers  of  the  com- 


LOGICAL  EXERCISES  317 

mon  broom  and  these  are  adapted  by  a  curious  mech- 
anism for  cross-fertilization.  When  a  bee  lights 
on  the  wing-petals  of  a  young  flower,  it  is  slightly 
opened,  and  the  short  stamens  spring  out,  which 
rub  their  pollen  against  the  abdomen  of  the  bee. 
If  a  rather  older  flower  is  visited  for  the  first  time 
(or  if  the  bee  exerts  great  force  on  a  younger 
flower),  the  keel  opens  along  its  whole  length,  and 
the  longer  as  well  as  the  shorter  stamens,  together 
with  the  much  elongated  curved  pistil,  spring  forth 
with  violence.  The  flattened  spoon-like  extremity 
of  the  pistil  rests  for  a  time  on  the  back  of  the 
bee,  and  leaves  on  it  the  load  of  pollen  with  which 
it  is  charged.  As  soon  as  the  bee  flies  away,  the 
pistil  instantly  curls  round,  so  that  the  stigmatic 
surface  is  now  upturned  and  occupies  a  position,  in 
which  it  would  be  rubbed  against  the  abdomen  of 
another  bee  visiting  the  same  flower.  Thus,  when 
the  pistil  first  escapes  from  the  keel,  the  stigma  is 
rubbed  against  the  back  of  the  bee,  dusted  with 
pollen  from  the  longer  stamens,  either  of  the  same 
or  another  flower ;  and  afterwards  against  the  lower 
surface  of  the  bee,  dusted  with  pollen  from  the 
shorter  stamens,  which  is  often  shed  a  day  or  two 
before  that  from  the  longer  stamens.  If  the  visits 
of  bees  are  prevented,  and  if  the  flowers  are  not 
dashed  by  the  wind  against  any  object,  the  keel 
never  opens,  so  that  the  stamens  and  pistil  remain 
enclosed.  Plants  thus  protected  yield  very  few 
pods  in  comparison  with  those  produced  by  neigh- 
boring uncovered  bushes,  and  sometimes  none  at 
all.  —  Darwin. 


318  INDUCTIVE  LOGIC 

15.  Baron  Zacli  received  a  letter  from  Pons,  a 
successful  finder  of  comets,  complaining  that  for  a 
certain  period  he  had  found  no  comets,  though  he 
had  sought  diligently.  Zach,  a  man  of  much  sly 
humor,  told  him  that  no  spots  had  been  seen  on 
the  sun  for  about  the  same  time  —  which  was  true 
—  and  assured  him  that  when  the  spots  came  back, 
the  comets  would  come  with  them.  Some  time 
after  that  he  got  a  letter  from  Pons,  who  informed 
him,  with  great  satisfaction,  that  he  was  quite 
right,  that  very  large  spots  had  appeared  on  the 
sun,  and  that  he  had  found  a  line  comet  shortly 
after.  —  De  Morgax's  Budget  of  Paradoxes. 

16.  If  Tellus  winged  be, 

The  earth  a  motion  round ; 
Then  much  deceived  are  they 

Who  nere  before  it  found. 
Solomon  was  the  wisest, 

His  wit  nere  this  attained ; 
Cease,  then,  Copernicus, 

Thy  hypothesis  vain ! 

—  Sylvanus  Morgax,  1652. 

17.  Weather  Forecaster  Dunn  has  prepared  a 
chart  showing  the  number  of  deaths  from  grip  in 
New  York  City  during  the  period  from  March  22 
to  May  16,  1891,  establishing  the  relation  between 
the  death-rates  and  weather  conditions  during  the 
grip  epidemic  of  that  year.  Mr.  Dunn  has  made  a 
careful  study  of  records  of  the  disease,  and  selected 
the  epidemic  of  1891  as  being  the  time  when  the 
grip  was  most  pronounced. 


LOGICAL  EXERCISES  319 

He  lias  apparently  demonstrated  that  the  weather 
is  an  important  factor  in  the  mortality  of  grip  cases. 
He  says  that  humidity  or  moisture  in  the  air  seems 
to  be  the  most  important  element  in  causing  the 
disease  to  spread.  There  is  a  corresponding  in- 
crease of  deaths  with  increasing  humidity. 

The  fatality  is  most  marked  when  the  humidity 
is  at  its  maximum  and  there  is  a  sudden  fall  of  the 
temperature.  This  is  shown  by  the  record  of  April 
21,  when  the  death-rate  from  grip  was  the  highest 
ever  known.  During  the  twenty-four  hours  of  that 
day  250  deaths  were  reported.  On  April  1  and 
April  30  the  death-rate  was  also  high.  These  were 
days  following  a  sudden  fall  in  temperature. 

All  through  the  epidemic  the  charts  show  an 
increasing  death-rate  with  high  or  increasing  hu- 
midity. The  higher  the  humidity  and  the  more 
sudden  the  fall  in  temperature,  the  greater  was  the 
number  of  deaths.  When  the  temperature  and  the 
humidity  dropped  at  the  same  time,  there  was  a  de- 
crease in  the  death-rate,  as  Mr.  Dunn  points  out  by 
several  examples.  He  says  that  the  lesson  to  be 
learned  from  his  chart  is  that  those  suffering  from 
an  incipient  attack  of  the  grip  should  be  most 
cautious  of  the  cold,  humid  days  that  immediately 
follow  the  warm,  damp  ones. 

18.  If  in  a  reservoir  immersed  in  water,  the  air 
be  compressed  to  the  extent  of  ten  atmospheres, 
and  supposing  that  now,  when  the  compressed  air 
has  acquired  the  temperature  of  the  water,  it  be 
allowed  to  act  upon  a  piston  loaded  by  a  weight, 
the  weight  is  raised.     At  the  same  time  the  water 


320  INDUCTIVE  LOGIC 

becomes  cooler,  showing  that  a  certain  quantity  of 
heat  had  disappeared  in  producing  the  mechanical 
effort  of  raising  the  weight. 

19.  That  the  feeling  of  effort  is  largely,  if  not 
entirely,  of  peripheral,  rather  than  central  origin, 
appears  from  such  experiments  as  the  following  :  — 

Hold  the  finger  as  if  to  pull  the  trigger  of  a  pis- 
tol. Think  vigorously  of  bending  the  finger,  but 
do  not  bend  it.  An  unmistakable  feeling  of  effort 
results.  Repeat  the  experiment,  and  notice  that 
the  breath  is  involuntarily  held,  and  that  there  are 
tensions  in  the  other  muscles.  Eepeat  the  experi- 
ment again,  taking  care  to  keep  the  breathing  regu- 
lar and  the  other  muscles  passive.  Little  or  no 
feeling  of  effort  will  now  accompany  the  imaginary 
bending  of  the  finger.  —  Eerrier. 

20.  As  to  the  nature  of  petrified  shells,  Quirini 
conceived  that  as  earthy  particles  united  in  the  sea 
so  as  to  form  the  shells  of  Mollusca,  the  same  crys- 
tallizing process  might  be  effected  on  the  land ;  and 
that  in  the  latter  case,  the  germs  of  the  animals 
might  have  been  disseminated  through  the  sub- 
stance of  the  rocks,  and  afterwards  developed  by 
virtue  of  humidity. 

21.  Voltaire  suggested  that  the  marine  shells 
found  on  the  tops  of  mountains  are  Eastern  species 
dropped  from  the  hats  of  pilgrims  as  they  returned 
from  the  Holy  Land. 

22.  The  epicyclical  theory  of  the  heavens  Avas 
confirmed  by  its  predicting  eclipses  of  the  sun  and 
moon,  configurations  of  the  planets,  and  other  celes- 
tial phenomena. 


LOGICAL  EXERCISES  321 

23.  Arfv^edsoii  discovered  lithia,  by  perceiving 
an  excess  of  weight  in  tlie  sulphate  produced  from 
a  small  x^ortion  of  what  he  considered  as  magnesia 
present  in  a  mineral  he  had  analyzed. 

24.  We  see  among  the  nebulae  (which  are  dif- 
fused along  the  Milky  Way)  instances  of  all  degrees 
of  condensation,  from  the  most  loosely  diffused 
fluid,  to  that  separation  and  solidification  of  parts 
by  which  suns  and  satellites  and  planets  are 
formed;  and  thus  we  have  before  us  instances  of 
systems  in  all  their  stages ;  as  in  a  forest  we  see 
trees  in  every  period  of  growth.  —  Laplace. 

25.  It  had  been  deductively  inferred  from  the 
Copernican  theory  that  the  planets,  Venus  and  Mer- 
cury, ought  to  pass  through  phases,  like  the  moon, 
and  the  telescope  revealed  this  to  be  the  case. 

26.  Werner,  says  Sir  Charles  Lyell,  had  not 
travelled  to  distant  countries ;  he  had  merely  ex- 
plored a  small  portion  of  Germany,  and  conceived, 
and  persuaded  others  to  believe,  that  the  whole  sur- 
face of  our  planet,  and  all  the  mountain  chains  in 
the  world,  were  made  after  the  model  of  his  own 
province. 

27.  Scheiner  was  a  monk ;  and  on  communicating 
to  the  superior  of  his  order  the  account  of  the  spots 
on  the  sun,  received  the  reply :  "  I  have  searched 
through  Aristotle,  and  can  find  nothing  of  the  kind 
mentioned :  be  assured,  therefore,  that  it  is  a  decep- 
tion of  your  senses,  or  of  your  glasses." 

28.  When  we  are  told  that  a  man  has  become 
deranged  from  anxiety  or  grief,  we  have  learned 
very  little  if  we  rest  content  with  that.     How  does 


322  INDUCTIVE  LOGIC 

it  happen  that  another  man,  subjected  to  an  ex- 
actly similar  cause  of  grief,  does  not  go  mad  ? — 
Maudsley. 

29.  It  was  a  general  belief  at  St.  Kilda  that  the 
arrival  of  a  ship  gave  all  the  inhabitants  colds.  Dr. 
John  Campbell  took  pains  to  ascertain  the  fact  and 
to  explain  it  as  the  effect  of  effluvia  arising  from 
human  bodies  ;  it  was  discovered,  however,  that  the 
situation  of  St.  Kilda  renders  a  northeast  wind  in- 
disi)ensably  necessary  before  a  ship  can  make  the 
landing. 

30.  Chrysippus  maintained  that  cock-fighting  was 
the  tinal  cause  of  cocks,  these  birds  being  made  by 
Providence  in  order  to  inspire  us  by  the  example  of 
their  courage. 

31.  Touch  in  succession  various  objects  on  the 
table.  A  paper-weight,  if  metallic,  is  usually  cold 
to  the  touch  ;  books,  paper,  and  especially  a  woollen 
table-cover,  comparatively  warm.  Test  them  by 
means  of  a  thermometer,  and  there  will  be  little  or 
no  difference  in  their  temperatures.  Why  then  do 
some  feel  cold,  others  warm  to  the  touch?  The 
sense  of  touch  does  not  inform  us  directly  of  tem- 
perature, but  of  the  rate  at  which  our  finger  gains  or 
loses  heat.  As  a  rule,  bodies  in  a  room  are  colder 
than  the  hand,  and  heat  always  tends  to  pass  from 
a  warmer  to  a  colder  body.  Of  a  number  of  bodies, 
all  equally  colder  than  the  hand,  that  one  will  seem 
coldest  to  the  touch,  as  the  metallic,  Avhich  is  able 
most  rapidly  to  convey  away  heat  from  the  hand. 
—  Tait. 

32.  One  of  Joule's  experiments  concerning  the 


LOGICAL   EXERCISES  323 

mechanical  value  of  light  is  as  follows:  He  com- 
pared the  heat  evolved  in  the  wire  conducting  a  gal- 
vanic current  when  the  wire  was  ignited  by  the 
passage  of  the  current,  with  that  evolved  when  with 
an  equal  current  it  was  kept  cool  by  immersion  in 
water.  These  experiments  showed  a  small  but  un- 
mistakable diminution  of  the  heat  when  light  also 
was  given  out.  —  Tait. 

33.  It  is  an  illusion  in  psychology  and  a  corrup- 
tion of  logic  to  take  the  conditions  which  occasion 
the  logical  operations  of  thought  for  the  operations 
themselves.  There  is  only  one  delusion  more  des- 
perate still,  —  to  imagine  that  a  complete  physical 
theory  of  the  nervous  system  will  explain  that 
which  is  itself  the  condition  of  any  theory  being 
possible  at  all.  —  Lotze. 

34.  During  the  retreat  of  the  Ten  Thousand  a 
cutting  north  wind  blew  in  the  faces  of  the  soldiers ; 
sacrifices  were  offered  to  Boreas,  and  the  severity  of 
the  wind  immediately  ceased,  which  seemed  a  proof 
of  the  god's  causation. 

35.  It  has  been  shown  by  observation  that  over- 
driven cattle,  if  killed  before  recovery  from  their 
fatigue,  become  rigid,  and  putrefy  in  a  surprisingly 
short  time.  A  similar  fact  has  been  observed  in  the 
case  of  animals  hunted  to  death,  cocks  killed  during 
a  fight,  and  soldiers  slain  in  battle.  The  contrary 
is  remarked  when  the  muscular  exercise  has  not 
been  great  or  excessive. 

36.  A  correct  analysis  of  lapis  lazuli  was  sus- 
pected to  be  erroneous  because  there  seemed  to  be 
nothing  in  the  elements  assigned  to  it,  which  were 


324  INDUCTIVE  LOGIC 

silica,  alumina,  soda,  sulphur,  and  a  trace  of  iron,  to 
account  for  the  brilliant  blue  color  of  the  stone. 

37.  According  to  the  theory  that  the  earth  has 
but  a  thin  crust,  it  is  still  substantially  a  liquid 
globe,  and  therefore,  under  the  attractive  influence 
of  the  sun  and  moon,  it  ought  to  behave  like  a  yield- 
ing liquid.  According  to  Hopkins,  Thomson,  and 
others,  the  earth  in  all  its  astronomical  relations  be- 
haves like  a  rigid  solid,  —  a  solid  more  rigid  than  a 
solid  globe  of  glass,  —  and  the  difference  between  the 
behavior  of  a  liquid  globe  and  a  solid  globe  could 
easily  be  detected  by  astronomical  phenomena. — 
Le  Coxte. 

38.  Many  years  ago  I  was  struck  with  the  fact 
that  bumblebees,  as  a  general  rule,  perforate  flowers 
only  when  these  grow  in  large  numbers  near  together. 
In  a  garden  where  there  were  some  very  large 
beds  of  Stachys  coccmea  and  of  Pentstemon  argutus, 
every  single  flower  was  perforated ;  but  I  found  two 
plants  of  the  former  species  growing  quite  separate 
with  their  petals  much  scratched,  showing  that  they 
had  been  frequently  visited  by  bees,  and  yet  not  a 
single  flower  was  perforated.  I  found  also  a  sepa- 
rate plant  of  the  Pentstemon,  and  saw  bees  entering 
the  mouth  of  the  corolla  and  not  a  single  flower  had 
been  perforated.  In  the  following  year  (1842)  I 
visited  the  same  garden  several  times :  on  the  19th 
of  July  humblebees  were  sucking  the  flowers  in  the 
proper  manner,  and  none  of  the  corollas  were  per- 
forated. On  the  7th  of  August  all  the  flowers  were 
perforated,  even  those  on  some  few  plants  of  the 
salvia,  which  grew  at  a  little  distance  from  the  great 


LOGICAL  EXERCISES  325 

bed.  On  the  21st  of  August  only  a  few  flowers  on 
the  summits  of  the  spikes  of  both  species  remained 
fresh,  and  not  one  of  these  was  now  bored.  Again, 
in  my  own  garden  every  plant  in  several  rows  of  the 
common  bean  had  many  flowers  perforated ;  but  I 
found  three  plants  in  separate  parts  of  the  garden 
which  had  sprung  up  accidentally,  and  these  had  not 
a  single  flower  perforated.  General  Strachey  for- 
merly saw  many  perforated  flowers  in  a  garden  in 
the  Himalaya,  and  he  wrote  to  the  owner  to  inquire 
whether  this  relation  between  the  plants  growing 
crowded  and  their  perforation  by  bees  there  held 
good,  and  was  answered  in  the  affirmative.  Hence 
it  follows  that  the  red  clover  and  the  common  bean 
when  cultivated  in  great  masses  in  fields.  Erica 
tetralix  growing  in  large  numbers  on  heaths,  — rows 
of  the  scarlet  kidney-bean  in  the  kitchen  garden,  — 
and  masses  of  any  species  in  the  flower  garden  are 
all  eminently  liable  to  be  perforated.  The  explana- 
tion of  this  is  not  difficult.  Flowers  growing  in 
large  numbers  attract  crowds  of  insects.  They  are 
thus  stimulated  to  work  quickly  by  rivalry.  Also 
many  flowers  have  their  nectaries  dry,  which  is  most 
quickly  discovered  by  biting  holes  in  them. — 
Charles  Darwin. 

39.  The  seat  of  sensation  is  in  the  heart,  as  it  is  in 
the  centre  of  the  body;  the  brain  is  cold  in  order 
that  it  may  counteract  the  heat  of  the  heart.  In  or- 
der to  temper  the  coldness  of  the  brain,  blood  is  con- 
veyed to  the  membrane  which  envelops  it  by  means 
of  veins  or  channels.  But,  lest  the  heat  so  conveyed 
should  injure  the  brain,  the  veins,  instead  of  being 


326  INDUCTIVE  LOGIC 

large  and  few,  are  small  and  many,  and  the  blood 
conveyed,  instead  of  being  copious  and  thick,  is 
thin  and  pure.  —  Aristotle. 

40.  The  lungs  of  a  fox  must  be  a  specific  for 
asthma,  because  that  animal  is  remarkable  for  its 
strong  powers  of  respiration.  —  Paris'  Pharmaco- 
logia. 

41.  G-alileo  discovered,  by  the  use  of  his  telescope, 
the  four  small  satellites  which  circulate  round  Jupi- 
ter. It  was  then  inferred  that  what  happened  on 
the  smaller  scale  might  also  be  found  true  of  the 
larger  planetary  system. 

42.  The  first  step  toward  the  discovery  of  photog- 
raphy was  the  knowledge  that  visual  light  caused 
a  chemical  change  in  iodide  of  silver.  The  second 
step  was  to  fix  in  permanent  position  the  portion 
of  the  substance  changed  by  the  light,  while  the 
unchanged  portion  was  removed. 

From  what  is  known  of  the  chemical  elements 
and  their  compounds,  it  seems  highly  probable 
that  numerous  compounds  may  exist  which  are 
sensitive  in  the  same  way  to  waves  of  entirely 
different  lengths  from  those  that  produce  vision. 
Even  with  the  salts  of  silver  it  has  long  been  known 
that  the  range  of  wave-lengths  capable  of  producing 
photographic  effect  is  much  greater  than  the  visual 
range;  and  that  the  wave-lengths  which  produce 
the  maximum  physiological  effect  (light)  are  not 
the  same  as  those  that  produce  the  maximum  photo- 
graphic effect. 

It  has  been  shown  by  Professor  S.  K,.  Langley 
that  flint  glass  is  transparent  to  waves  about  four 


LOGICAL  EXERCISES  327 

times  as  long  as  the  longest  in  the  visual  range; 
and  that  rock-salt  is  transparent  to  a  range  below 
the  reel  end  of  the  visible  spectrum  twenty-nine 
times  as  long  as  the  entire  visual  range.  Glass  is 
opaque  to  very  short  waves,  its  limit  in  that  direc- 
tion being  nearly  coincident  with  the  visual  limit. 
Quartz,  on  the  other  hand,  is  transparent  to  a  range 
of  short  waves  extending  far  beyond  the  visual 
limit,  but  is  opaque  to  very  short  waves.  May  not 
these  substances  prove  valuable  in  this  new  field 
of  actinography,  as  quartz  trains  have  proved  in 
photographing  the  ultra-violet  spectrum  ? 

Should  the  report  of  this  discovery  (Rontgen's) 
be  confirmed,  we  cannot  fail  to  accord  the  highest 
praise  to  this  new  triumph  of  science,  and  to  pre- 
dict a  development  of  the  new  field  of  actinography 
that  may  prove  of  greater  importance  than  pho- 
tography. 

From  the  analogy  between  this  form  of  radiant 
energy  and  dark  heat  it  might  appropriately  be 
called  "  dark  light."  —  The  Electrical  World. 

43.  As  to  the  theory  of  geyser-eruption,  the 
following  principles  have  been  established.  The 
boiling-point  of  Avater  rises  as  the  pressure  in- 
creases, being  293°  for  a  pressure  of  four  atmos- 
pheres. Also,  if  the  pressure  be  diminished  when 
the  water  is  under  very  strong  pressure,  the  water 
will  immediately  flash  into  steam.  Moreover,  if 
the  circulation  is  impeded,  as  when  the  water  is 
contained  in  long,  narrow,  irregular  tubes,  and 
heated  with  great  rapidity,  the  boiling-point  will 
be  reached  below  while  it  is  far  from  this  point  in 


328  INDUCTIVE  LOGIC 

the  upper  part  of  the  tube.  Therefore  at  the  mo- 
ment of  eruption,  the  boiling-point  for  the  lowest 
depth  is  actually  reached.  The  water  there  being 
transferred  into  steam,  the  expanding  steam  would 
lift  the  whole  column  of  water  in  the  tube,  causing 
an  overflow.  This  would  diminish  the  pressure  in 
every  part  of  the  tube,  and  consequently  a  large 
quantity  of  water  before  very  near  the  boiling-point 
would  flash  into  steam  and  instantly  eject  the 
whole  of  the  water  in  the  pipe,  the  steam  rushing 
out  immediately  afterwards.  The  premonitory  can- 
nonading beneath  is  evidently  produced  by  the 
collapse  of  large  steam-bubbles  rising  through  the 
cooler  part  of  the  water  of  the  tube.  —  Buxsex's 
Theory. 

44.  Mackenzie's  theory  of  geyser-eruption  is 
that  the  geyser  pipe  is  connected  by  a  narrow  con- 
duit Avith  the  lower  part  of  a  subterranean  cave, 
w^hose  walls  are  heated  by  the  near  vicinity  of 
volcanic  fires.  The  water  rising  above  the  opening 
of  the  conduit,  and  changing  into  steam,  and  having 
no  way  of  escape,  would,  through  pressure  thus 
caused,  be  forced  up  the  pipe,  and  the  steam  rushing 
after  it.  Professor  Le  Conte  says  of  this  theory :  If 
there  were  but  one  geyser,  this  would  be  considered 
a  very  ingenious  and  probable  hypothesis ;  for  we 
may  conceive  of  a  cave  and  a  conduit  so  constructed 
as  to  account  for  the  phenomena.  But  there  are  so 
many  geysers,  that  it  is  inconceivable  that  all  of 
them  should  have  caves  and  conduits  so  peculiarly 
constructed.  This  theory,  therefore,  is  entirely  un- 
tenable. 


LOGICAL  EXERCISES  329 

45.  It  has  been  found  by  experiment  that  a 
current  moving  at  the  rate  of  three  inches  per 
second  will  take  up  and  carry  along  fine  clay; 
moving  six  inches  per  second,  will  carry  fine  sand ; 
eight  inches  per  second,  coarse  sand  the  size  of  lin- 
seed; twelve  inches,  gravel;  twenty-four  inches, 
pebbles ;  three  feet,  angular  stones  of  the  size  of  a 
hen's  egg.  It  will  be  readily  seen  that  the  carry- 
ing power  increases  much  more  rapidly  than  the 
velocity.  For  instance,  a  current  of  twelve  inches 
per  second  carries  gravel,  while  a  current  of  three 
feet  per  second,  only  three  times  greater  velocity, 
carries  stones  many  hundred  times  as  large  as 
grains  of  gravel. 

46.  If  wood  be  soaked  in  a  strong  solution  of 
sulphate  of  iron  (copperas)  and  dried,  and  the  same 
process  be  repeated  until  the  wood  is  highly  charged 
with  this  salt,  and  then  burned,  the  structure  of  the 
wood  will  be  preserved  in  the  peroxide  of  iron  left. 
Also,  it  is  well  known  that  the  smallest  fissures  and 
cavities  in  rocks  are  speedily  filled  by  infiltrating 
waters  with  mineral  matters.  Now,  Avood  buried 
in  soil  soaked  with  some  petrifying  material  becomes 
highly  charged  with  the  same,  and  the  cells  filled 
with  infiltrated  matter,  and  when  the  wood  decays 
the  petrifying  material  is  left,  retaining  the  struct- 
ure of  the  wood.  In  nature  also  there  is  an  addi- 
tional process,  not  illustrated  by  the  experiment, 
or  by  the  example  of  infiltrated  fillings.  As  each 
particle  of  organic  matter  passes  away  by  decay,  a 
particle  of  mineral  matter  takes  its  place,  until 
finally  the  whole  of  the  organic  matter  is  replaced. 


330  INDUCTIVE  LOGIC 

47.  As  to  the  origin  of  bitumen,  the  following 
observations  have  been  made :  Certain  organic 
matters  at  ordinary  temperature,  in  presence  of 
abundant  moisture,  and  out  of  contact  of  air,  will 
undergo  a  species  of  decomposition  or  fermentation 
by  which  an  oily  or  tarry  substance,  similar  to  bitu- 
men, is  formed.  In  the  interior  of  heaps  of  vegetable 
substance,  such  bituminous  matter  is  often  found. 
Fossil  cavities  have  been  found  in  solid  limestone 
containing  bitumen,  evidently  formed  by  decompo- 
sition of  the  animal  matter.  vSo,  also,  shales  have 
been  found  in  Scotland,  filled  with  fishes  which 
have  changed  into  bitumen. 

48.  Count  llumford  in  1798  proved  that  the  com- 
mon notion  that  heat  was  a  substance  was  false,  by 
boring  a  large  piece  of  brass,  under  great  pressure 
of  the  borer,  whilst  the  brass  was  in  a  gallon  of 
water;  and  at  the  end  of  two  and  one  half  hours 
the  water  actually  boiled. 

49.  Kenelm  Digby's  treatment  of  wounds  was  to 
apply  an  ointment,  not  to  the  wound  itself,  but  to 
the  sword  that  had  inflicted  it,  to  dress  this  care- 
fully at  regular  intervals,  and  in  the  meantime, 
having  bound  up  the  wound,  to  leave  it  alone  for 
seven  days.  It  was  observed  that  many  cures  fol- 
lowed upon  this  treatment. 

50.  When  Pascal's  barometer  was  carried  to  the 
top  of  Puy-de-Dome,  and  the  mercury  in  it  fell,  it 
was  inferred  that  the  fall  of  the  mercury  was  due 
to  the  change  in  elevation.  Before  finally  accepting 
this  conclusion,  the  barometer  was  placed  in  exposed 
positions  and  in  sheltered,  when  the  wind  blew  and 


LOGICAL  EXERCISES  331 

when  it  was  calm,  in  rain  and  in  fog ;  and  these 
varying  circumstances  did  not  materially  affect  the 
result. 

51.  A  French  experimenter,  Pouchet,  thought  he 
had  obtained  indubitable  evidence  of  spontaneous 
generation.  He  took  infusions  of  vegetable  matter, 
boiled  them  to  a  pitch  sufficient  to  destroy  all  germs 
of  life,  and  hermetically  sealed  the  liquid  in  glass 
flasks.  After  an  interval,  micro-organisms  appeared. 
It  seems  that  at  a  certain  stage  in  Pouchet's  process, 
he  had  occasion  to  dip  the  mouths  of  the  flasks  in 
mercury.  It  occurred  to  Pasteur,  in  repeating  the 
experiments,  that  germs  might  have  found  their 
way  in  from  the  atmospheric  dust  on  the  surface  of 
this  mercury.  And  when  he  carefully  cleansed  the 
surface  of  the  mercury,  no  life  appeared  afterwards 
in  his  flasks. 

52.  The  causes  to  which  the  decay  of  the  natives 
of  New  Zealand  has  been  assigned  are  given  as  fol- 
lows :  drink,  disease,  European  clothing,  peace,  and 
wealth.  —  Journal  of  the  Anthropological  Institute. 

53.  An  eminent  judge  was  in  the  habit  of  jocosely 
propounding,  after  dinner,  a  theory  that  the  cause 
of  the  prevalence  of  Jacobinism  was  the  practice 
of  bearing  three  names.  He  quoted,  on  one  side, 
Charles  James  Fox,  E-ichard  Brinsley  Sheridan, 
John  Home  Tooke,  John  Philpot  Curran,  Samuel 
Taylor  Coleridge,  Theobald  Wolfe  Tone.  On  the 
other  hand  there  were,  William  Pitt,  John  Scott, 
William  Windham,  Samuel  Horsley,  Henry  Dun- 
das,  Edmund  Burke.  Moreover,  the  practice  of 
giving  children  three  names   has  been  a  growing 


332  INDUCTIVE  LOGIC 

practice,  and  Jacobinism  lias  also  been  growing. 
The  practice  of  giving  children  three  names  is  more 
common  in  America  than  in  England.  In  England, 
we  still  have  a  King  and  a  House  of  Lords  ;  but  the 
Americans  are  Republicans.  Burke  and  Theobald 
Wolfe  Tone  are  both  Irishmen;  therefore  the  be- 
ing an  Irishman  is  not  the  cause  of  Jacobinism. 
Horsley  and  Home  Tooke  are  both  clergymen; 
therefore  the  being  a  clergyman  is  not  the  cause  of 
Jacobinism.  Fox  and  Windham  were  both  educated 
at  Oxford  ;  therefore  the  being  educated  at  Oxford 
is  not  the  cause  of  Jacobinism.  Pitt  and  Home 
Tooke  were  both  educated  at  Cambridge  ;  therefore 
the  being  educated  at  Cambridge  is  not  the  cause  of 
Jacobinism.  The  cause  is,  therefore,  the  having 
three  names. — Macaulay. 

54.  The  exotic  Pelargonia  have  a  peculiar  herring- 
bone structure  in  the  petals ;  moreover,  the  herring- 
bone structure  is  conjoined  in  the  Pelargonia  with 
the  general  characteristics  of  the  Geranieae.  Also 
the  flowers  with  such  seed-vessels  as  our  wild  gera- 
niums have  the  characters  of  Geraniese.  It  is,  there- 
fore, exceedingly  probable  that  our  wild  geraniums 
should  have  the  pecidiar  herring-bone  structure. 

55.  Colonies  ought  not  to  rebel  against  the 
mother  country,  since  they  are  its  children  and 
children  ought  not  to  rebel  against  their  parents. 

56.  Eluding  that  the  size  of  towns  varies  con- 
comitantly with  the  size  of  the  rivers  on  which  they 
are  built,  an  observer  might  infer  that  the  size  of 
the  river  was  due  to  the  size  of  the  town. 

57.  An  eminent  author,  writing  on  the  work  of 


LOGICAL  EXERCISES  333 

the  English  Church  before  the  Tractariaii  move- 
ment, contrasts  the  newer  state  of  things  unfavor- 
ably with  the  older,  because  the  Church  in  those 
former  clays  taught  us  to  use  religion  as  a  light 
by  which  to  see  our  way  along  the  road  of  duty. 
Without  the  sun  our  eyes  would  be  of  no  use  to  us ; 
but  if  we  look  at  the  sun,  we  are  simply  dazzled  and 
can  see  neither  it  nor  anything  else.  It  is  precisely 
the  same  with  theological  speculations.  If  the  bea- 
con lamp  is  shining,  a  man  of  healthy  mind  will 
not  discuss  the  composition  of  the  flame. 

58.  Scarlet  color  prevails  among  balsamina, 
Euphorbia,  Pelargonium,  poppy,  Salvia,  Bouvardia, 
and  Verbena,  yet  none  of  the  scarlets  are  of  sweet 
perfumes.  Some  of  the  light-colored  balsams  and 
verbenas  are  sweet-scented,  but  none  of  the  scarlets 
are.  The  common  sage  with  blue  blooms  is  odorif- 
erous both  in  flower  and  foliage;  but  the  scarlet 
salvias  are  devoid  of  smell.  None  of  the  sweet- 
scented-leaved  Pelargoniums  have  scarlet  blooms, 
and  none  of  the  scarlet  bloomers  have  sweet  scent 
of  leaves  nor  of  blooms.  Some  of  the  white- 
margined  poppies  have  pleasant  odors;  but  the 
British  scarlets  are  not  sweet-scented.  The  British 
white-blooming  hawthorn  is  of  the  most  delightful 
fragrance;  the  scarlet  flower  has  no  smell.  Some 
of  the  honeysuckles  are  sweetly  perfumed,  but  the 
scarlet  trumpet  is  scentless. 

59.  The  productive  powers  of  plants,  judging 
from  the  increased  fertility  of  the  parent-plants 
and  from  the  increased  powers  of  growth  in  the 
offspring,  are  favored  by  some  degree  of  differen- 


334  INDUCTIVE  LOGIC 

tiation  in  the  elements  which  interact  and  unite 
so  as  to  form  a  new  being.  Here  w^e  have  some 
analogy  with  chemical  affinity  or  attraction,  which 
comes  into  play  only  between  atoms  or  molecules 
of  a  different  nature.  As  Professor  Miller  re- 
marks :  "  Generally  speaking,  the  greater  the  dif- 
ference in  the  properties  of  two  bodies,  the  more 
intense  is  their  tendency  to  mutual  chemical  action. 
But  between  bodies  of  a  similar  character  the  ten- 
dency to  unite  is  feeble." 

60.  In  affirming  that  the  growth  of  the  body  is 
mechanical,  and  that  thought,  as  exercised  by  us, 
has  its  correlative  in  the  physics  of  the  brain,  I 
think  the  position  of  the  "  materialist  "  is  stated,  as 
far  as  that  position  is  a  tenable  one.  I  think  the 
materialist  will  be  able  finally  to  maintain  this  po- 
sition against  all  attacks ;  but  I  do  not  think,  in 
the  present  condition  of  the  human  mind,  that  he 
can  pass  beyond  this  position.  I  do  not  think  he  is 
entitled  to  say  that  his  molecular  groupings  and  his 
molecular  motions  explain  everything.  In  reality, 
they  explain  nothing.  The  utmost  he  can  affirm  is 
the  association  of  the  two  classes  of  phenomena,  of 
whose  real  bond  of  union  he  is  in  absolute  ignorance. 
The  problem  of  the  connection  of  body  and  soul  is  as 
insoluble  in  its  modern  form  as  it  was  in  the  presci- 
entiiic  ages.  Phosphorus  is  known  to  enter  into  the 
composition  of  the  human  brain,  and  a  trenchant 
German  writer  has  exclaimed,  "Ohne  Phosphor, 
kein  Gedanke  !  "  That  may  or  may  not  be  the  case  ; 
but  even  if  we  knew  it  to  be  the  case,  the  knowledge 
would  not  lighten  our  darkness.  —  Tyndall. 


LOGICAL  EXERCISES  335 

61.  G-ranting  that  Hegel  was  more  or  less  success- 
ful in  constructing,  a  priori,  the  leading  results  of 
the  moral  sciences,  still  it  was  no  proof  of  the  correct- 
ness of  the  hypothesis  of  identity,  with  which  he 
started.  The  facts  of  nature  would  have  been  the 
crucial  test.  That  in  the  moral  sciences  traces  of 
the  activity  of  the  human  intellect  and  of  the  several 
stages  of  its  development  should,  present  them- 
selves, was  a  matter  of  course ;  but  surely,  if  nature 
really  reflected  the  result  of  the  thought  of  a  cre- 
ative mind,  the  system  ought,  without  difficulty,  to 
find  a  place  for  her  comparatively  simple  phenomena 
and  processes.  —  Helmholtz. 

62.  When  young  Galileo  was  a  student  at  Pisa, 
he  noticed  one  day,  during  the  service  at  the  great 
Cathedral,  the  chandelier  swinging  backwards  and 
forwards,  and  convinced  himself,  by  counting  his 
pulse,  that  the  duration  of  the  oscillations  was 
independent  of  the  arc  through  which  it  moved. 

63.  Goethe  enunciated  the  existence  of  a  resem- 
blance between  the  different  parts  of  one  and  the 
same  organic  being.  According  to  Goethe's  own 
account,  the  idea  first  occurred  to  him  while  looking 
at  a  fan-palm  at  Padua.  He  was  struck  by  the  im- 
mense variety  of  changes  of  form  which  the  succes- 
sively developed  stem-leaves  exhibit,  by  the  way  in 
which  the  first  simple  root  leaflets  are  replaced  by 
a  series  of  more  and  more  divided  leaves,  till  w^e 
come  to  the  most  comx^licated.  He  afterwards  suc- 
ceeded in  discovering  the  transformation  of  stem- 
leaves  into  sepals  and  petals,  and  of  sepals  and 
petals  into  stamens,  nectaries,  and  ovaries,  and  thus 


336  INDUCTIVE  LOGIC 

he  was  led  to  the  doctrine  of  the  metamorphosis  of 
plants  which  he  published  in  1790. 

64.  A  fortunate  glance  at  a  broken  sheep's-skull, 
which  Goethe  found  by  accident  on  the  sand  of  the 
Lido  at  Venice,  suggested  to  him  that  the  skull  it- 
self consisted  of  a  series  of  very  much  altered  verte- 
brae. At  first  sight  no  two  things  can  be  more  un- 
like than  the  broad,  uniform,  cranial  cavity  of  the 
mammalia,  enclosed  by  smooth  plates,  and  the  nar- 
row cylindrical  tube  of  the  spinal  marrow,  composed 
of  short,  massy,  jagged  bones.  —  Helmholtz. 

6d.  The  existence  of  the  so-called  blind  spot  in 
the  eye  was  first  demonstrated  by  theoretical  argu- 
ments. While  the  long  controversy  whether  the 
perception  of  light  resided  in  the  retina  or  the 
choroid  was  still  undecided,  Mariotte  asked  himself 
what  perception  there  was  where  the  choroid  is 
deficient.  He  made  experiments  to  discover  this 
point  and  in  the  course  of  them  discovered  the 
blind  spot. 

66.  Haliy  observed  that  crystals  of  "heavy  spar" 
from  Sicily  and  those  from  Derbyshire  (which  were 
considered  to  be  the  same  substance)  differed  in  their 
angles  of  cleavage  by  three  and  one-half  degrees,  and 
remarked:  "I  could  not  suppose  that  this  difference 
was  the  effect  of  any  law  of  decrement ;  for  it  would 
have  been  necessary  to  suppose  so  rapid  and  complex 
a  law,  that  such  a  hypothesis  might  have  been  justly 
regarded  as  an  abuse  of  the  theory."  Vauquelin 
by  chemical  analysis  discovered  that  the  base  of 
the  crystals  from  Sicily  was  strontia,  and  that  of 
those  from  Derbyshire  was  baryta.     These   facts, 


LOGICAL  EXERCISES  337 

becoming  known  to  Haiiy,  enabled  him  by  inference 
to  discover  that  the  angles  of  crystals  might  be 
employed  as  a  test  for  the  presence  of  different 
substances  which  very  nearly  resemble  each  other 
in  other  respects. 

67.  Graebe,  a  German  chemist,  in  investigating 
a  class  of  compounds,  called  the  quinones,  deter- 
mined incidentally  the  molecular  structure  of  a 
body  closely  resembling  alizarine,  which  had  been 
discovered  several  years  before.  This  body  was 
derived  from  naphthaline,  and,  like  many  similar 
derivatives,  was  reduced  back  to  naphthaline  when 
heated  with  zinc-dust.  This  circumstance  led  the 
chemist  to  heat  also  madder  alizarine  with  zinc- 
dust,  when,  to  his  surprise,  he  obtained  anthracene. 
Of  course,  the  inference  was  at  once  drawn  that 
alizarine  must  have  the  same  relation  to  anthracene 
that  the  allied  coloring  matter  bore  to  naphtha- 
line; and,  more  than  this,  it  was  also  inferred 
that  the  same  chemical  processes  which  produced 
the  coloring  matter  from  naphthaline  when  applied 
to  anthracene  would  yield  alizarine.  The  result 
fully  answered  these  expectations,  and  now  ali- 
zarine is  manufactured  on  a  large  scale  from  an- 
thracene obtained  from  coal-tar.  —  Cooke,  The  New 
Chemistry. 

68.  Sir  Charles  Lyell,  by  studying  the  fact  that 
the  river  Ganges  yearly  conveys  to  the  ocean  as 
much  earth  as  would  form  sixty  of  the  great  pyra- 
mids of  Egypt,  was  enabled  to  infer  that  the  ordi- 
nary slow  causes  now  in  operation  upon  the  earth 
would  account  for  the  immense  geological  changes 


338  INDUCTIVE  LOGIC 

that  have  occurred,  without  having  recourse  to  the 
less  reasonable  theory  of  sudden  catastrophes. 

69.  Joule's  experiments  show  that  when  heat  is 
produced  by  the  consumption  of  work,  a  definite 
quantity  of  work  is  required  to  produce  that  amount 
of  heat  which  is  known  to  the  physicists  as  the  unit 
of  heat ;  the  heat,  that  is  to  say,  which  is  necessary 
to  raise  one  gramme  of  water  through  one  degree 
centigrade.  The  quantity  of  w^ork  necessary  for 
this  is,  according  to  Joule's  best  experiments,  equal 
to  the  work  which  a  gramme  would  perform  in  fall- 
ing through  a  height  of  425  metres. 

In  order  to  show^  how  closely  concordant  are  his 
numbers,  I  will  adduce  the  results  of  a  few  series 
of  experiments  which  he  obtained  after  introduc- 
ing the  latest  improvements  in  his  methods. 

(1)  A  series  of  experiments  in  w^hich  water  was 
heated  by  friction  in  a  brass  vessel.  In  the  interior 
of  this  vessel  a  vertical  axle  provided  with  sixteen 
paddles  was  rotated,  the  eddies  thus  produced  being 
broken  by  a  series  of  projecting  barriers,  in  which 
parts  were  cut  out  large  enough  for  the  paddles  to 
pass  through.  The  value  of  the  equivalent  was 
424.9  metres. 

(2)  Two  similar  experiments,  in  which  mercury 
in  an  iron  vessel  was  substituted  for  water  in  a 
brass  one,  gave  425  and  426.3  metres  respectively. 

(3)  Two  series  of  experiments,  in  which  a 
conical  ring  rubbed  against  another,  both  sur- 
rounded by  mercury,  gave  426.7  and  425.6  metres 
respectively. 

Exactly  the   same   relations   between  heat  and 


LOGICAL  EXERCISES  339 

work  were  also  found  in  the  reverse  process ;  that 
is,  when  work  was  produced  by  heat.  —  Helmholtz. 

70.  A  gas  which  is  allowed  to  expand  with  mod- 
erate velocity  becomes  cooled.  Joule  was  the  first 
to  show  the  reason  of  this  cooling.  For  the  gas  has, 
in  expanding,  to  overcome  the  resistance  which  the 
X)ressure  of  the  atmosphere  and  the  slowly  yielding 
sides  of  the  vessel  oppose  to  it ;  or,  if  it  cannot  of 
itself  overcome  this  resistance,  it  supports  the  arm 
of  the  observer,  which  does  it.  Gas  thus  performs 
work,  and  this  work  is  produced  at  the  cost  of  its 
heat.  Hence  the  cooling.  If,  on  the  contrary,  the 
gas  is  suddenly  allowed  to  issue  into  a  perfectly  ex- 
hausted space  where  it  finds  no  resistance,  it  does 
not  become  cool,  as  Joule  has  shown. —  Helmholtz. 

71.  The  principal  feature  in  the  plan  of  my  at- 
tempt to  penetrate  into  the  North  Polar  region,  or 
if  possible  to  cross  it,  is,  in  brief,  to  try  to  make  use 
of  the  currents  of  the  sea,  instead  of  fighting  against 
them.  My  opinion  is,  as  I  have  already  explained 
on  several  occasions,  that  there  must  somewhere 
run  currents  into  the  Polar  region,  which  carry  the 
floe-ice  across  the  Polar  Sea,  first  northward  toward 
the  Pole,  and  then  southward  again  into  the  Atlan- 
tic Ocean.  That  these  currents  really  exist  all 
Arctic  expeditions  prove,  as  most  of  them  have  had 
to  fight  against  the  currents  and  against  the  ice 
drifting  southward,  because  they  have  tried  to  get 
northward  from  the  wrong  side.  I  think  a  very 
simple  conclusion  must  be  drawn  from  this  fact  that 
currents  and  drifting  ice  are  constantly  coming  from 
the  unknown  north,  viz. :  Currents  and  perhaps  also 


340  INDUCTIVE  LOGIC 

ice  must  x^ass  into  tins  same  region,  as  the  water 
running  out  must  be  replaced  by  water  running  in. 
This  conclusion  is  based  upon  the  simplest  of  all 
natural  laws ;  but  there  seem  to  be  people  who  will 
not  even  admit  the  necessity  of  this. 

That  such  currents  run  across  the  North  Polar 
region  is  also  proved  by  many  facts.  I  may  men- 
tion the  great  quantities  of  Siberian  driftwood  which 
are  annually  carried  to  the  shores  of  Spitzbergen 
and  Greenland;  it  comes  in  such  abundance  and 
with  such  regularity  that  it  is  quite  impossible  it 
should  be  carried  to  these  shores,  so  far  from  the 
original  home,  by  occasional  winds  or  currents. 
There  must  be  a  regular  communication  between 
the  coasts  of  Siberia  and  those  of  Spitzbergen  and 
Greenland.  By  this  same  communication  were 
several  objects  from  the  unfortunate  Jeannette  car- 
ried to  the  Greenland  coast.  The  Jeannette  sank 
in  June,  1881,  to  the  north  of  the  New  Siberian 
Islands,  and  three  years  afterward,  in  June,  1884,  a 
great  many  objects  belonging  to  her  or  her  crew 
were  found  on  an  ice-floe  on  the  southwest  coast  of 
Greenland.  This  floe  can  only  have  been  brought 
there  by  the  same  current  which  carries  the  drift- 
wood. By  this  same  current  an  Esquimau  imple- 
ment, a  throwing-stick  or  harpoon-thrower,  was  also 
carried  the  long  way  from  Alaska  to  the  west  coast 
of  Greenland.  There  can,  in  my  opinion,  be  no 
doubt  of  the  existence  of  such  a  communication  or 
current  across  the  North  Polar  region  from  the 
Siberian  side  to  the  Greenland  side.  —  Dk.  Nansen 
in  The  Strand  Magazine. 


INDEX 


Adams,  147. 

Adverbial  probability,  232. 

Aggregates,  Probability  as  af- 
fecting, 234  ff. 

Agreement,  Method  of,  84, 86  ff ., 
104,  128,  259,  275. 

Algebraical  logic,  219. 

Analogy,  35,  39  ff.,  44  if.,  202, 
204  ff.,  283,  291. 

Analysis,  (50,  62,  186. 

Apperception,  3,  266. 

Aquapendente,  211. 

Arithmetical  method,  37. 

Aristotle  16,  46,  50,  304. 

Association  of  ideas,  267. 

Astronomy,  284. 

Attention,  265. 

B. 

Bacon,  Francis,  16,  46,  72,  73, 
94,  163,  199,  267,  269,  271,  275, 
276,  300,  .303,  304,  309,  311. 

Bacon,  Roger,  300. 

Bain,  16,  220. 

Barrett,  61,  264. 

Basis  of  probability,  232. 

Ben  eke,  36. 

Beudant,  141. 

Biology,  216,  284. 

Bkintschli,  294,  296. 

Boole,  219. 

Bosanquet,  7,  26,  27,  29,  40,  42, 
58,  81,  312. 


Botany,  283. 
Boyle,  104,  132. 
Bradley,  22. 
Brahe',  Tycho,  76,  304. 
Brewster,  40,  97,  98. 
Brown,  59. 
Bullen,  247. 
Bunsen,  150,  245. 


Caesalpinus,  304. 

Calculation      of      probability, 

230  fe. 
Campanella,  303. 
Causal  analysis,  35,  40,  42,  45, 

47,  60,  64  ff. 
Causation,  45  ff.,  47,  50  ff.,  209, 

227,  228. 
Chalmers,  69. 
Chance,  240,  245  ff. 
Chemical  combinations,  71. 
Cbemistry,  288. 
Chenevix,  266. 

Circumstantial  evidence,  247. 
Classification,  206  ff.,  279,  283. 
Clifford,  50,  164-166,  172,  218. 
Coexistence,  66,  92,  258. 
Coincidence,  245,  246. 
Collocation,  68,  69,  255,  256. 
Combinations,     Theory    of    in 

causal  analysis,  77  ff.,  105. 
Concept,  90,  91,  205. 
Conceptual  processes,  Fallacies 

of,  263,  275  ff. 


341 


342 


INDEX 


Coucoraitant  variations.Method 

of,  84,  85,  130  ff. 
Conservation  of  energy,  52  ff., 

71,  72,  288  ff. 
Consilience  of  inductions,  198. 
Content,  explicit  and  implicit, 

6. 
Co-operative  circumstances,  69. 
Copernicus,  304. 
Correlations,  67. 
Counteracting  cause,  70. 
Counter-probability,  231. 
Cuvier,  9. 

D. 

Darwin,  Charles,  68,  77,  113, 
123, 126, 139, 141, 154, 161, 175, 
181,  187,  213,  215,  218,  241. 

Darwin,  G.  H.,  111. 

Davy,  Sir  Humphry,  149,  206, 
273. 

Deduction  and  induction,  16  ff., 
27. 

Deductive  method,  147. 

DeMorgan,  74. 

Derivative  laws,  253,  254. 

Descartes,  219. 

Development,  68,  218. 

Difference,  Method  of,  79,  84, 
85,  101  ff.,  117,  149. 

Discovery,  202. 

Duhamel,  28. 


E. 

Elimination,  90. 

Ellis,  213. 

Empirical  basis  of  probability, 

232. 
Empirical  laws,  38,  252,  276. 
Enumeration,    43,    45  ff.,    91; 

228  ff. 
Epistemology,  26,  58. 
Ethics,  295. 


Experiment,  10,  77  ff.,  97,  176, 

282. 
Explanation,  14. 
Explanation,  Historical,  291. 
Explicit  content,  6  ff. 


Fact  and  truth,  19,  20. 
Fallacies,  262  ff. 
Faraday  61,   74,   112-114,   160, 
166,  169,   205,   217,   268,  273. 
Fictions,  196. 

Final  cause.    See  Teleology. 
Florens,  223. 
Forel,  114. 
Franklin,  Benjamin,  44. 

G. 

Galileo,  302,  304. 
Generalization,  23,  48,  49,  107, 

204,  205,  256  ff.,  275  ff. 
Geology,  284  ff. 
Gide,  144,  241. 
Gilbert,  304, 
Glauber,  155. 
Gore,  167,   177,   206,   211,   264, 

266. 
Graber,  115. 
Green,  13,  45,  50,  58. 
Guyot,  97. 

H. 

Halley,  152,  159. 

Harvey,  211,  225. 

Hatchette,  141. 

Hegel,  294. 

Heraclitus,  270. 

Herschel,  59,  73,  149,  152,  217, 

275,  308  ff. 
Hippocrates,  223. 
Historical  explanation,  291. 
Holland,  217. 
Hume,  4,  53-55. 
Huyghens,  158. 


INDEX 


343 


Hypothesis,  42,  93,  174  ff.,  21G, 

271  ff.,  284,  308. 
Hypothetical  universal,  31. 


Idols  of  Bacon,  269  fp. 
Imagination,  185, 202, 263, 271  ff. 
Implicit  content,  6  ff. 
Increment  of  probability,  233, 

234. 
Induction  and  deduction,  16  ff. 
Inducto-deduetive  method,  156 

ff.,  282. 
Inductive  hazard,  24. 
Inference,  1  ff. 
Instances,  Number  of,  42. 
Insurance,  240. 
Intermixture  of  effects,  59. 
Invariability  of  causation,  51, 

54,  58. 
Inverse  problem,  27. 


James,  10. 

Janet,  209,  210,  211,  224. 

Jenkin,  72,  164,  165. 

Jenner,  177,  222. 

Jevons,    27-29,   115,    143,    170, 

206-208,  217,  236,  246,  312. 
Joint  method,  84,  85,  117  ff. 
Joule,  167. 
Judgment,    Fallacies    of,    263 

266  ff. 
Jurisprudence,  293  f . 


Kant,  53. 

Kepler,  76,  199,  304,  310. 
Kircher,  217. 
Kirchhoff,  245. 


Ladd,  294. 
Laplace,  153,  179. 


Lavater,  18. 

Law,  30,  31. 

Leonardo  da  Vinci,  32,  301. 

Le  Verrier,  147. 

Linnaeus,  217. 

Lister,  219. 

Locke,  16,  307. 

Lockyer,  208. 

Lotze,  22,  25,  26,  29,  31,  46,  58, 

109,  188,  189,  312. 
Loua,  241. 
Lubbock,  83,  114,  120,  124  ff., 

195,  212,  213. 
Lyell,  138,  182. 

M. 

Malthus,  219,  256. 

Mansel,  57. 

Mathematical  method,  172,  173. 

Mechanical  combination,  70. 

Medicine,  99,  100. 

Mill,  J.  S.,  16,  25,  30,  54-57,  59, 
68,  72,  79,  84,  86, 129, 156, 201, 
202,  220,  254,  260,  298,  309. 

Minto,  312. 

Molar  forces,  71. 

Molecular  forces,  71. 

N. 

Natural  kinds,  67,  205,  206. 
Negation,    Determination    by, 

78  ff.,  104. 
Negative  conditions,  70. 
Newman,  J.  H.,  312. 
Newton,  39, 153, 158, 159, 179,307. 
]^on  causa  pro  causa,  267. 

O. 

Observation,  72  ff.,  91,  227. 
Owen,  215. 


Pasteur,  98,  99,  160. 
Perception,  2  ff. 


344 


INDEX 


Perception,  Fallacies  of,  263  ff. 
Perfect  induction,  3(3  ff. 
Physics,  282. 
Plateau,  115,  125. 
Plato,  50,  297. 
Plurality  of  causes,  59,  93. 
Political  economy,  292  ff. 
Post  hoc  ergo  propter  hoc,  59, 

267. 
Postulate,  Fundamental,  8,  26, 

189  ff.,  261. 
Potential  cause,  66,  108. 
Potential  in  inference,  11. 
Prediction,  156  ff. 
Presentation,  Data  of,  5. 
Preyer,  .56. 
Priestley,  108. 

Probability,  29, 38, 43,  56,  226  ff . 
Proof,  202. 
Psychology   and    logic,    2    ff., 

14,  15,  47.  62,  133,  232,  262  ff., 

279,  289  ff. 
Psychology  and  history,  291  ff. 
Psychology,  Method  in,  294. 

Q. 
Quantitative  determination,  72, 

131  ff.,  282. 
Quetelet,  236. 


Railroad  accidents,  236  ff. 
Reality,  Inference  an  indirect 

reference  to,  13. 
Reduction,  28,  42. 
Residues,  84,  85,  146  ff. 
Ricardo,  132. 
Romanes,  200. 
Rule,  30. 

S. 

Saigey,  89,  135. 
Saint-Pierre,  224. 
Schleiermacher,  16. 


Schwann,  219. 

Science,  33. 

Sciences    and     the    inductive 

method,  281  ff. 
Scientific  analysis.    See  Causal 

analysis. 
Scientific  spirit,  33,  164,  201. 
Sequence,  64  ff.,  92. 
Sidgwick,  268. 
Sig\yart,  26,  29,  57,  58,  68,  94, 

107,  202,  312. 
Similarity,  Law  of,  205. 
Smith,  Adam,  268. 
Socrates,  297. 
Spencer,  257,  284-286. 
Spinoza,  187. 
Sprengel,  213. 
Sufficient  reason,  58. 
Suggestion  of  causal  relation, 

99,  224. 
Synthesis,  186. 
System,  7  ff.,  12,  17  ff.,  44,  45, 

58,  148,  176,  209,  211,  266. 


T. 

Tait,  52,  133.  151,  153,  159,  168, 

177,  180,  107. 
Teleology,  208  ff.,  222  ff.,  278. 
Telesius,  302. 
Tennyson,  12,  51. 
Thomson,  133,  151,  153. 
Totality,  Law  of,  7. 
Truth  and  fact,  19,  20. 
Tyndall,  75,  76,  80,  81,  102,  135, 

166,  183,  185,  217. 


U. 

Ueberweg,  32,  43,  58,  274,  300. 
Ultimate  laws,  253,  254. 
Uniformity  of  nature,  22,   25, 

51,.".4ff. 
Universal,  12,  18,  275. 
Universal  causation,  51. 


INDEX 


U5 


Venn,  29,  57,  77,  100,  111,  18(3, 

2(50,  312. 
Verification,  156  ff. 
Voltaire,  223. 

W. 

Waitmann,  205. 
Wallace,  191. 


Weber's  law,  72,  143. 

Whately,  57,  311. 

Whewell,  30,  198,  201,  202,  273, 

301,  302,  310. 
Wollaston,  266. 


Zoology,  283. 


Date  Due                          : 

Mr  1  4  '2 

9 

1 

1 

^ 

BC91.H62 
Inductive  logic; 

Princeton  Theological  Seminary-Speer  Library 


1    1012  00008  2877 


